The Less Wrong community is rather well-read, so this community-maintained list of recommendations on the best textbooks to read on a given subject should be pretty good.

Why textbooks though? In short: they’re *optimized for learning new material*. The fact that this sounds obvious only underlines how inconsistent you’d be if you declared yourself a “lover of knowledge” who “wants to know as much as possible” and yet spurns textbooks (or at least spends far less time reading them than you should) because they’re “not as exciting as the stuff out there”. Yep, this is partly a self-reminder. Luke:

For years, my self-education was stupid and wasteful. I learned by consuming blog posts, Wikipedia articles, classic texts, podcast episodes, popular books, video lectures, peer-reviewed papers, Teaching Company courses, and Cliff’s Notes. How inefficient!

I’ve since discovered that

textbooksare usually the quickest and best way to learn new material. That’s what they aredesignedto be, after all.

But there are good textbooks, and there are bad textbooks. Luke again:

I was forced to read some awful textbooks in college. The ones on American history and sociology were memorably bad, in my case. Other textbooks are exciting, accurate, fair, well-paced, and immediately useful.

Commenter RobinZ (in a thread discussing whether old texts in which now-standard ideas first appeared were worth reading):

Many textbooks are straightforwardly

badly written, to the point that the thirty-year-old conference papers in the citations are actuallymore accurate.

On to the list then. What I liked about it was the ground rules Luke stated at the outset to ensure high-quality recommendations. It led to rather non-standard suggestions like e.g. *not* reading Griffiths for electrodynamics or Russell for western philosophy or Mankiw for macroeconomics or Rudin for analysis even Jaynes for Bayesian probability theory, texts normally considered classic must-reads in their respective fields:

- Post the title of your favorite textbook on a given subject.
- You must have read at least two other textbooks on that same subject.
- You must briefly name the other books you’ve read on the subject and explain why you think your chosen textbook is superior to them.

The list itself – enjoy!

*The Best Textbooks on Every Subject*

- On
**history of western philosophy**, lukeprog recommends Melchert’s*The Great Conversation*over Russell’s*A History of Western Philosophy*, Copelston’s*History of Philosophy*, and Kenney’s*A New History of Western Philosophy*. - On
**cognitive science**, lukeprog recommends Bermudez’s*Cognitive Science*over Thagard’s*Mind: Introduction to Cognitive Science*and Kolak’s*Cognitive Science*. - On
**introductory logic for philosophy**, lukeprog recommends Lepore’s*Meaning and Argument*over Copi’s*Introduction to Logic*, Hurley’s*A Concise Introduction to Logic*, and Smith’s*An Introduction to Formal Logic*. - On
**economics**, michaba03m recommends Mankiw’s*Macroeconomics*over Varian’s*Intermediate Microeconomics*and Katz & Rosen’s*Macroeconomics*. - On
**economics**, realitygrill recommends McAfee’s*Introduction to Economic Analysis*over Mankiw’s*Macroeconomics*and Case & Fair’s*Principles of Macroeconomics*. - On
**representation theory**, SarahC recommends Sternberg’s*Group Theory and Physics*over Lang’s*Algebra*, Weyl’s*The Theory of Groups and Quantum Mechanics*, and Fulton & Harris’*Representation Theory: A First Course*. - On
**statistics**, madhadron recommends Kiefer’s*Introduction to Statistical Inference*over Hogg & Craig’s*Introduction to Mathematical Statistics*, Casella & Berger’s*Statistical Inference*, and others. - On
**advanced Bayesian statistics**, Cyan recommends Gelman’s*Bayesian Data Analysis*over Jaynes’*Probability Theory: The Logic of Science*and Bernardo’s*Bayesian Theory*. - On
**basic Bayesian statistics**, jsalvatier recommends Skilling & Sivia’s*Data Analysis: A Bayesian Tutorial*over Gelman’s*Bayesian Data Analysis*, Bolstad’s*Bayesian Statistics*, and Robert’s*The Bayesian Choice*. - On
**real analysis**, paper-machine recommends Bartle’s A Modern Theory of Integration over Rudin’s*Real and Complex Analysis*and Royden’s*Real Analysis*. - On
**non-relativistic quantum mechanics**, wbcurry recommends Sakurai & Napolitano’s*Modern Quantum Mechanics*over Messiah’s*Quantum Mechanics*, Cohen-Tannoudji’s*Quantum Mechanics*, and Greiner’s*Quantum Mechanics: An Introduction*. - On
**music theory**, komponisto recommends Westergaard’s*An Introduction to Tonal Theory*over Piston’s*Harmony*, Aldwell and Schachter’s*Harmony and Voice Leading*, and Kotska and Payne’s*Tonal Harmony*. - On
**business**, joshkaufman recommends Kaufman’s*The Personal MBA: Master the Art of Business*over Bevelin’s*Seeking Wisdom*and Munger’s*Poor Charlie’s Alamanack*. - On
**machine learning**, alexflint recommends Bishop’s*Pattern Recognition and Machine Learning*over Russell & Norvig’s*Artificial Intelligence: A Modern Approach*and Thrun et. al.’s*Probabilistic Robotics*. - On
**algorithms**, gjm recommends Cormen et. al.’s*Introduction to Algorithms*over Knuth’s*The Art of Computer Programming*and Sedgwick’s*Algorithms*. - On
**electrodynamics**, Alex_Altair recommends Griffiths’*Introduction to Electrodynamics*over Jackson’s*Electrodynamics*and Feynman’s*Lectures on Physics*. - On
**electrodynamics**, madhadron recommends Purcell’s*Electricity and Magnetism*over Griffith’s*Introduction to Electrodynamics*, Feynman’s*Lectures on Physics*, and others. - On
**systems theory**, Davidmanheim recommends Meadows’*Thinking in Systems: A Primer*over Senge’s*The Fifth Discipline: The Art & Practice of The Learning Organization*and Kim’s*Introduction to Systems Thinking*. - On
**self-help**, lukeprog recommends Weiten, Dunn, and Hammer’s*Psychology Applied to Modern Life*over Santrock’s*Human Adjustment*and Tucker-Ladd’s*Psychological Self-Help*. - On
**probability theory**, SarahC recommends Feller’s*An Introduction to Probability Theory*+*Vol. 2*over Ross’*A First Course in Probability*and Koralov & Sinai’s*Theory of Probability and Random Processes*. - On
**probability theory**, madhadron recommends Grimmett & Stirzaker’s*Probability and Random Processes*over Feller’s*Introduction to Probability Theory and Its Applications*and Nelson’s*Radically Elementary Probability Theory*. - On
**topology**, jsteinhardt recommends Munkres’*Topology*over Armstrong’s*Topology*and Massey’s*Algebraic Topology*. - On
**linguistics**, etymologik recommends O’Grady et al.’s*Contemporary Linguistics*over Hayes et al.’s*Linguistics: An Introduction to Linguistic Theory*and Carnie’s*Syntax: A Generative Introduction*. - On
**meta-ethics**, lukeprog recommends Miller’s*An Introduction to Contemporary Metaethics*over Jacobs’*The Dimensions of Moral Theory*and Smith’s*Ethics and the A Priori*. - On
**decision-making & biases**, badger recommends Bazerman & Moore’s*Judgment in Managerial Decision Making*over Hastie & Dawes’*Rational Choice in an Uncertain World*, Gilboa’s*Making Better Decisions*, and others. - On
**neuroscience**, kjmiller recommends Bear et al’s*Neuroscience: Exploring the Brain*over Purves et al’s*Neuroscience*and Kandel et al’s*Principles of Neural Science*. - On
**World War II**, Peacewise recommends Weinberg’s*A World at Arms*over Churchill’s*The Second World War*and Day’s*The Politics of War*. - On
**elliptic curves**, magfrump recommends Koblitz’*Introduction to Elliptic Curves and Modular Forms*over Silverman’s*Arithmetic of Elliptic Curves*and Cassel’s*Lectures on Elliptic Curves*. - On
**improvisation**, Arepo recommends Salinsky & Frances-White’s*The Improv Handbook*over Johnstone’s*Impro*, Johnston’s*The Improvisation Game*, and others. - On
**thermodynamics**, madhadron recommends Hatsopoulos & Keenan’s*Principles of General Thermodynamics*over Fermi’s*Thermodynamics*, Sommerfeld’s*Thermodynamics and Statistical Mechanics*, and others. - On
**statistical mechanics**, madhadron recommends Landau & Lifshitz’*Statistical Physics, Volume 5*over Sethna’s*Entropy, Order Parameters, and Complexity*and Reichl’s*A Modern Course in Statistical Physics*. - On
**criminal justice**, strange recommends Fuller’s*Criminal Justice: Mainstream and Crosscurrents*over Neubauer & Fradella’s*America’s Courts and the Criminal Justice System*and Albanese’*Criminal Justice*. - On
**organic chemistry**, rhodium recommends Clayden et al’s*Organic Chemistry*over McMurry’s*Organic Chemistry*and Smith’s*Organic Chemistry*. - On
**special relativity**, iDante recommends Taylor & Wheeler’s*Spacetime Physics*over Harris’*Modern Physics*, French’s*Special Relativity*, and others. - On
**abstract algebra**, Bundle_Gerbe recommends Dummit & Foote’s*Abstract Algebra*over Lang’s*Algebra*and others. - On
**decision theory**, lukeprog recommends Peterson’s*An Introduction to Decision Theory*over Resnik’s*Choices*and Luce & Raiffa’s*Games and Decisions*. - On
**calculus**, orthonormal recommends Spivak’s*Caclulus*over Thomas’*Calculus*and Stewart’s*Calculus*. - On
**analysis in R**, orthonormal recommends Strichartz’s^{n}*The Way of Analysis*over Rudin’s*Principles of Mathematical Analysis*and Kolmogorov & Fomin’s*Introduction to Real Analysis*. - On
**real analysis and measure theory**, orthonormal recommends Stein & Shakarchi’s*Measure Theory, Integration, and Hilbert Spaces*over Royden’s*Real Analysis*and Rudin’s*Real and Complex Analysis*. - On
**partial differential equations**, orthonormal recommends Strauss’*Partial Differential Equations*over Evans’*Partial Differential Equations*and Hormander’s*Analysis of Partial Differential Operators*. - On
**introductory real analysis**, SatvikBeri recommends Pugh’s Real Mathematical Analysis over Lang’s*Real and Functional Analysis*and Rudin’s*Real and Complex Analysis*. - On
**commutative algebra**, SatvikBeri recommends MacDonald’s*Introduction to Commutative Algebra*over Lang’s*Algebra*and Eisenbud’s*Commutative Algebra With a View Towards Algebraic Geometry*. - On
**animal behavior**, Natha recommends Alcock’s*Animal Behavior, 6th edition*over Dugatkin’s*Principles of Animal Behavior*and newer editions of the Alcock textbook.

You’re probably hungry for explanations for some of these non-standard suggestions. The community list I’ve linked to above has them all in the discussion section, but here’s a sampling to titillate and excite!

Subject: History of Western Philosophy

Recommendation:The Great Conversation, 6th edition, by Norman Melchert

Reason: The most popular history of western philosophy is Bertrand Russell’sA History of Western Philosophy, which is exciting but also polemical and inaccurate. More accurate but dry and dull is Frederick Copelston’s 11-volumeA History of Philosophy. Anthony Kenny’s recent 4-volume history, collected into one book asA New History of Western Philosophy, is both exciting and accurate, but perhaps too long (1000 pages) and technical for a first read on the history of philosophy. Melchert’s textbook,The Great Conversation, is accurate but also the easiest to read, and has the clearest explanations of the important positions and debates, though of course it has its weaknesses (it spends too many pages on ancient Greek mythology but barely mentions Gottlob Frege, the father of analytic philosophy and of the philosophy of language). Melchert’s history is also the only one to seriously cover the dominant mode of Anglophone philosophy done today: naturalism (what Melchert calls “physical realism”). Be sure to get the 6th edition, which has major improvements over the 5th edition.

Subject: Cognitive Science

Recommendation:Cognitive Science, by Jose Luis Bermudez

Reason: Jose Luis Bermudez’sCognitive Science: An Introduction to the Science of Minddoes an excellent job setting the historical and conceptual context for cognitive science, and draws fairly from all the fields involved in this heavily interdisciplinary science. Bermudez does a good job of making himself invisible, and the explanations here are some of the clearest available. In contrast, Paul Thagard’sMind: Introduction to Cognitive Scienceskips the context and jumps right into a systematic comparison (by explanatory merit) of the leading theories of mental representation: logic, rules, concepts, analogies, images, and neural networks. The book is only 270 pages long, and is also more idiosyncratic than Bermudez’s; for example, Thagard refers to the dominant paradigm in cognitive science as the “computational-representational understanding of mind,” which as far as I can tell is used only by him and people drawing from his book. In truth, the term refers to a set of competing theories, for example the computational theory and therepresentational theory. While not the best place to start, Thagard’s book is a decent follow-up to Bermudez’s text. Better, though, is Kolak et. al.’sCognitive Science: An Introduction to Mind and Brain. It contains more information than Bermudez’s book, but I prefer Bermudez’s flow, organization and content selection. Really, though, both Bermudez and Kolak offer excellent introductions to the field, and Thagard offers a more systematic and narrow investigation that is worth reading after Bermudez and Kolak.

Subject: Introductory Logic for Philosophy

Recommendation:Meaning and Argumentby Ernest Lepore

Reason: For years, the standard textbook on logic was Copi’sIntroduction to Logic, a comprehensive textbook that has chapters on language, definitions, fallacies, deduction, induction, syllogistic logic, symbolic logic, inference, and probability. It spends too much time on methods that are rarely used today, for example Mill’s methods of inductive inference. Amazingly, the chapter on probability does not mention Bayes (as of the 11th edition, anyway). Better is the current standard in classrooms: Patrick Hurley’sA Concise Introduction to Logic.It has a table at the front of the book that tells you which sections to read depending on whether you want (1) a traditional logic course, (2) a critical reasoning course, or (3) a course on modern formal logic. The single chapter on induction and probability moves too quickly, but is excellent for its length. Peter Smith’s An Introduction to Formal Logic instead focuses tightly on the usual methods used by today’s philosophers: propositional logic and predicate logic. My favorite in this less comprehensive mode, however, is Ernest Lepore’sMeaning and Argument, because it (a) is highly efficient, and (b) focuses not so much on the manipulation of symbols in a formal system but on the arguably trickier matter of translating English sentences into symbols in a formal system in the first place.

Subject:Representation Theory

Recommendation: Group Theory and Physics by Shlomo Sternberg.This is a remarkable book pedagogically. It is the most extremely, ridiculously concrete introduction to representation theory I’ve ever seen. To understand representations of finite groups you literally start with crystal structures. To understand vector bundles you think about vibrating molecules. When it’s time to work out the details, you literally work out the details, concretely, by making character tables and so on. It’s unique, so far as I’ve read, among math textbooks on any subject whatsoever, in its shameless willingness to draw pictures, offer physical motivation, and give examples with (gasp)

literal numbers.Math for dummies? Well, actually, it

isrigorous, just not as general as it could potentially be. Also, many people’s optimal learning style is quite concrete; I believe your first experience with a subject should be example-based, to fix ideas. After all, when you were a kid you played around with numbers long before you defined the integers. There’s something to the old Dewey idea of “learning by doing.” And I have only seen it triedoncein advanced mathematics.Fulton and Harris won’t do this. The representation theory section in Lang’s

Algebrawon’t do this — it starts about three levels of abstraction up and stays there. Weyl’s classicThe Theory of Groups and Quantum Mechanicsisn’t actually the best way to learn — the group theory and the physics are in separate sections and both are a little compressed and archaic in terminology. Sternberg is really a different thing entirely: it’s almost more like having a teacher than reading a textbook.The treatment is really most relevant for physicists, but

even if you’re not a physicist(and I’m not), if you have general interest in math, and background up to a college abstract algebra course, you should check this out just to see what unusually clear, intuitive mathematical writing looks like. It willmake you happy.

Music theory:An Introduction to Tonal Theoryby Peter Westergaard.Comparing this book to others is almost unfair, because in a sense, this is the only book on its subject matter that has ever been written. Other books purporting to be on the same topic are really on another, wrong(er) topic that is properly regarded as superseded by this one.

However, it’s definitely worth a few words about what the difference is. The approach of “traditional” texts such as Piston’s

Harmonyis to come up with a historically-based taxonomy (and a rather awkward one, it must be said) of common musical tropes for the student to memorize. There is hardly so much as an attempt at non-fakeexplanation, and certainly no understanding of concepts like reductionism or explanatory parsimony. The best analogy I know would be trying to learn a language from a phrasebook instead of a grammar; it’s a GLUT approach to musical structure.(Why is this approach so popular? Because it doesn’t require much abstract thought, and is easy to give students tests on.)

Not all books that follow this traditional line are quite as bad as Piston, but some are even worse. An example of not-quite-so-bad would be Aldwell and Schachter’s

Harmony and Voice Leading; an example of even-worse would be Kotska and Payne’sTonal Harmony, or pretty much anything you can find in a non-university bookstore (that isn’t a reprint of some centuries-old classic like Fux).

Topic: Introductory Bayesian Statistics (as distinct from more advanced Bayesian statistics)

Recommendation:Data Analysis: A Bayesian Tutorialby Skilling and SiviaWhy: Sivia’s book is well suited for smart people who have not had little or no statistical training. It starts from the basics and covers a lot of important ground. I think it takes the right approach, first doing some simple examples where analytical solutions are available or it is feasible to integrate naively and numerically. Then it teaches into maximum likelihood estimation (MLE), how to do it and why it makes sense from a Bayesian perspective. I think MLE is a very very useful technique, especially so for engineers. I would overall recommend just Part I: The Essentials, I don’t think the second half is so useful, except perhaps the MLE extensions chapter. There are better places to learn about MCMC approximation.

Why not other books?

Bayesian Data Analysisby Gelman – Geared more for people who have done statistics before.

Bayesian Statisticsby Bolstad – Doesn’t cover as much as Sivia’s book, most notably doesn’t cover MLE. Goes kinda slowly and spends a lot of time on comparing Bayesian statistics to Frequentist statistics.

The Bayesian Choice– more of a mathematical statistics book, not suited for beginners.

Subject: Problem Solving

Recommendation: Street-Fighting Mathematics The Art of Educated Guessing and Opportunistic Problem Solving

Reason: So, it has come to my attention that there is a freely available .pdf for the textbook for the MIT course Street Fighting Mathematics. It can be found here. I have only been reading it for a short while, but I would classify this text as something along the lines of ‘x-rationality for mathematics’. Considerations such as minimizing the number of steps to solution minimizes the chance for error are taken into account, which makes it very awesome.in any event, I feel that this should be added to the list, maybe under problem solving? I’m not totally clear about that, it seems to be in a class of its own.

Seemingly relevant comparison volumes:

Numbers Rule Your World: The Hidden Influence of Probabilities and Statistics on Everything You Do

Back-of-the-Envelope Physics

How Many Licks? Or, How to Estimate Damn Near Anything

Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin

Subject:Introductory Decision Making/Heuristics and Biases

Recommendation:Judgment in Managerial Decision Making by Max Bazerman and Don Moore.This book wins points by being comprehensive, including numerous exercises to demonstrate biases to the reader, and really getting to the point. Insights pop out at every page without lots of fluffy prose. The recommendations are also more practical than other books.

Alternatives:

- Rational Choice in an Uncertain World by Reid Hastie and Robyn Dawes. A good, well-rounded alternative. Its primary weakness is the lack of exercises.
- Making Better Decisions: Decision Theory in Practice by Itzhak Gilboa. Filled with exercises, this book would be a great supplement to a course on this subject, but it wouldn’t stand alone on self-study. This book specializes in probability and quantitative models, so it’s not as practical, but if you’ve read Bazerman and Moore, read this next if you want to see more of the economic/decision theory approach.
- How to Think Straight about Psychology by Keith Stanovich. Slanted towards what science is and how to perform and evaluate experiments, this is still a decent introduction.
- Smart Choices by John Hammond, Ralph Keeney, and Howard Raiffa. Not recommended. Few studies cited and few technical insights, if my memory is correct. The book doesn’t go far beyond “clarify your problem, your objectives, and the possible alternatives”.

Introduction to Neuroscience

Recommendation:Neuroscience:Exploring the Brain by Bear, Connors, Paradiso

Reasons:BC&P is simply much better written, more clear, and intelligible than it’s competitorsNeuroscienceby Dale Purves andFundamentals of Neural Scienceby Eric Kandel. Purves covers almost the same ground, but is just not written well, often just listing facts without really attempting to synthesize them and build understanding of theory. Bear is better than Purves in every regard. Kandel is the Bible of the discipline, at 1400 pages it goes into way more depth than either of the others, and way more depth than you need or will be able to understand if you’re just starting out. It is quite well-written, but it should be treated more like an encyclopedia than a textbook.I also can’t help recommending

Theoretical Neuroscienceby Peter Dayan and Larry Abbot, a fantastic introduction to computational neuroscience,Bayesian Brain, a review of the state of the art of baysian modeling of neural systems, andNeuroeconomicsby Paul Glimcher, a survey of the state of the art inthatfield, which is perhaps the most relevant of all of this to LW-type interests. The second two are the only books of their kind, the first has competitors inComputational Explorations in Cognitive Neuroscienceby Randall O’Reilly andFundamentals of Computational Neuroscienceby Thomas Trappenberg, but I’ve not read either in enough depth to make a definitive recommendation.

Calculus:Spivak’s Calculus over Thomas’ Calculus and Stewart’s Calculus. This is a bit of an unfair fight, because Spivak is an introduction to proof, rigor, and mathematical reasoning disguised as a calculus textbook; but unlike the other two, reading it is actually exciting and meaningful.

Analysis in R^n (not to be confused with Real Analysis and Measure Theory):Strichartz’s The Way of Analysis over Rudin’s Principles of Mathematical Analysis, Kolmogorov and Fomin’s Introduction to Real Analysis(yes, they used the wrong title; they wrote it decades ago). Rudin is a lot of fun if you already know analysis, but Strichartz is a much more intuitive way to learn it in the first place. And after more than a decade, I still have trouble reading Kolmogorov and Fomin.

Real Analysis and Measure Theory (not to be confused with Analysis in R^n):Stein and Shakarchi’s Measure Theory, Integration, and Hilbert Spaces over Royden’s Real Analysis and Rudin’s Real and Complex Analysis. Again, I prefer the one that engages with heuristics and intuitions rather than just proofs.

Partial Differential Equations:Strauss’ Partial Differential Equations over Evans’ Partial Differential Equationsand Hormander’s Analysis of Partial Differential Operators. Donotread the Hormander book until you’ve had a full course in differential equations, and want to suffer; the proofs are of the form “Apply Theorem 3.5.1 to Equations (2.4.17) and (5.2.16)”. Evans is better, but has a zealot’s disdain of useful tools like the Fourier transform for reasons of intellectual purity, and eschews examples. By contrast, Strauss is all about learning tools, examining examples, and connecting to real-world intuitions.

Business:The Personal MBA: Master the Art of Businessby Josh Kaufman.I’m the author, so feel free to discount appropriately. However, the entire reason I wrote this book is because I spent

yearssearching for a comprehensive introductory primer on business practice, and I couldn’t find one – so I created it.Business is a critically important subject for rationalists to learn, but most business books are either overly-narrow, shallow in useful content, or overly self-promotional. I’ve read thousands of them over the past six years, including textbooks.

Business schools typically fragment the topic into several disciplines, with little attempt to integrate them, so textbooks are usually worse than mainstream business books. It’s possible to read business books for years (or graduate from business school) without ever forming a clear understanding of what businesses fundamentally

are, or how they actually work.If you’re familiar with Charlie Munger’s “mental model” approach to learning, you’ll recognize the approach of

The Personal MBA– identify and master the set of business-related mental models that will actually help you operate a real business successfully.Because making good decisions requires rationality, and businesses are created by people, the book spend just as much time on evolutionary psychology, decision-making in the face of uncertainty, and anti-akrasia as it does on traditional business topics like marketing, sales, finance, etc.

Peter Bevelin’s

Seeking Wisdomis comparable, but extremely dry and overly focused on investment vs. actually running a business. The Munger biographyPoor Charlie’s Almanackcontains some helpful details about Munger’s philosophy and approach, but is not comprehensive.If anyone has read another solid, comprehensive primer on general business practice, I’d love to know.

Subject: Introductory Real (Mathematical) Analysis:

Recommendation: Real Mathematical Analysis by Charles PughThe three

introductoryAnalysis books I’ve read cover-to-cover are Lang’s, Pugh’s, and Rudin’s.What makes Pugh’s book stand out is simply that he focuses on building up repeatedly useful machinery and concepts-a broad set of theorems that are clearly motivated and widely applicable to a lot of problems. Pugh’s book is also chock-full of examples, which make understanding the material much faster. And finally, Pugh’s book has a very large number of exercises of varying difficulty-Pugh has more than 500 exercises total.

In contrast, Rudin’s book tends to focus on “magic.” Rudin uses the shortest possible proofs for a given theorem. The problem is that the shortest proofs aren’t necessarily the most instructive-while Baby Rudin is a beautiful work of Math qua Math, it’s not a particularly good book to learn from.

Finally, Lang’s book is frankly subpar. Lang leaves out critical details of some proofs (dismissing one 6 page proof as trivial!), is poorly motivated by examples, and has a number of mistakes.

If you want to really understand Mathematical Analysis and get to the point where you can use the concepts to create proofs and solve problems, Pugh is the best book on the topic. If you want a concise summary of undergraduate analysis to review, pick Rudin’s book.

And if you’ve made it this far, here’s a cool positive-feedback-loop-style last one!

While the following isn’t really a textbook, I highly recommend it for helping you to improve your skill as a reader. “How to Read a Book” by Mortimer Adler and Charles Van Doren. It covers a variety of different techniques from how to analytically take apart a book to inspectional techniques for getting a quick overview of a book.

I never knew how to read analytically, I had never been taught any techniques for actually learning from a book. I always just assumed you read through it passively.

It has a fairly large appendix (~70 pgs) of recommended reading and sample tests/examples at the end of the book. It also has several sections on reading subject specific matter i.e. How to read History, Philosophy, Science, Practical books, etc. It also covers agreeing or disagreeing with an author, fairly criticizing a book, aids to reading. I think reading strategies may have been too narrow a choice of words. It really covers the “Art of Reading”. A good set of English classes would probably cover similar ground, although I didn’t see anything like this in my high school or undergraduate education.