# 100 Best Topology Books of All Time

We've researched and ranked the best topology books in the world, based on recommendations from world experts, sales data, and millions of reader ratings. Learn more

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

**A contrarian argues that modern physicists' obsession with beauty has given us wonderful math but bad science.**

Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to... more

Barbara KiserThis is a firecracker of a book—a shot across the bows of theoretical physics. Sabine Hossenfelder, a theoretical physicist working on quantum gravity and blogger, confronts failures in her field head-on. (Source)

*Euler's Gem*tells the illuminating story of this indispensable mathematical idea.

From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed... more

**Don't have time to read the top Topology books of all time? Read Shortform summaries.**

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Anne-Marie SlaughterLinked is about how to understand the world in terms of networks. To understand network science the first thing to do is to visualise the world the way you visualise the Internet or even the universe – hubs of infinitely intersecting networks. As the author says, everything can be reduced to links and nodes. This book is a very accessible introduction to the science of networks and to how to... (Source)

Bill BarhydtWritten before Facebook, this book predicts what the world will look like with amazing precision. (Source)

Originally drawn to Yaqui Indian spiritual leader don Juan Matus for his knowledge of mind-altering plants, bestselling author Carlos Castaneda soon immersed himself in the sorcerer’s magical world entirely. Ten years after his first encounter with the shaman, Castaneda examines his field notes and comes to understand what don Juan knew all along—that these plants are merely a means to understanding the alternative realities that one cannot fully embrace on one’s own. In... more

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

**Don't have time to read the top Topology books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

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**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
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*Bulletin of the American Mathematical Society*upon the 1955 publication of John L. Kelley's

*General Topology.*This comprehensive treatment for beginning graduate-level students immediately found a significant audience, and it remains a highly worthwhile and relevant book for students of topology and for professionals in many areas.

A systematic exposition of the part of general topology that has proven useful in several branches of mathematics, this... more

*This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincar� and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries...*more

Eric WeinsteinFolks frequently ask “What are the books that changed your life?” If I tell them, they are usually radically disappointed. I find that curious. I just cleared out of an office, and these are 4 shelves of spines of books that mattered enough to me to bring home. So here they are. (Source)

**Don't have time to read the top Topology books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

**The scion of a political dynasty ushers in the era of big government**

Politics was in Benjamin Harrison's blood. His great-grandfather signed the Declaration and his grandfather, William Henry Harrison, was the ninth president of the United States. Harrison, a leading Indiana lawyer, became a Republican Party champion, even taking a leave from the Civil War to campaign for Lincoln. After a scandal-free term in the Senate-no small feat in the Gilded Age-the Republicans chose Harrison as their presidential candidate in 1888. Despite losing the popular vote, he trounced the... more

**Cohomology of Groups**introduces students to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology. The basics of the subject are given (along with exercises) before the author discusses more specialized topics. less

Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes... more

This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional... more

Customary topics of point-set topology include metric... more

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**This book is your comprehensive workbook for Daily Math Practice Grade 4 (Common Core Math).**

By practicing and mastering this entire workbook, your child will become very familiar and comfortable with the state math exam and common core standards. This Daily Math Practice Grade 4... more

**Don't have time to read the top Topology books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

With a thoroughly modern point of view, it is the first truly new textbook in topology since Spanier, almost 25 years ago. Although the book is... more

More than 40 million students have trusted Schaum's Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum's Outlines cover everything from math to science, nursing to language. The main feature for all these books is the solved problems. Step-by-step, authors walk readers through coming up with solutions to exercises in their topic of choice. 391 solved problems 356 supplementary problems Teaches effective problem-solving Outline format supplies a concise... more

**Don't have time to read the top Topology books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

**Pure Mathematics for Beginners**

**Pure Mathematics for Beginners**consists of a series of lessons in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra.The 16 lessons in this book cover basic through intermediate material from each of these 8 topics. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively.Pure Mathematics for Beginners is perfect for

professors teaching an introductory college course in higher... more

* Provides a comprehensive... more

The purpose of this book is to put together in one place the basic elementary techniques for solving problems in maxima and minima other than the methods of calculus and linear programming. The emphasis is not on the individual problems, but on methods that solve large classes of problems. The many chapters of the book can be read independently, without references to what precedes or follows. Besides the many problems solved in the book, others are left to the reader to solve, with sketches of solutions given in the later pages.

less*Higher Topos Theory*, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. more

While containing all the key results of basic topology, Essential Topology never allows itself to get mired in details. Instead, the focus throughout is on providing interesting... more

**Don't have time to read the top Topology books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

The present book grew out of notes for an introductory topology course at the University of Alberta. It provides a concise introduction to set theoretic topology (and to a tiny little bit of algebraic topology). It is accessible to undergraduates from the second year on, but even beginning graduate... more

**Ten amazing curves personally selected by one of today's most important math writers**

*Curves for the Mathematically Curious*is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an account of the history and definition of a curve, providing a glimpse into the elegant and often surprising mathematics involved in its creation and evolution. In telling the ten stories, Havil introduces many mathematicians and other innovators, some whose fame has withstood the... more

*Elements of Algebraic Topology*provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for comunicating complex topics and the fun nature of algebraic topology for beginners. less

More than 40 million students have trusted Schaum's to help them... more

J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which... more

**Don't have time to read the top Topology books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including:

a treatment of the Baker Campbell Hausdorff formula and its use in place of... more

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Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological... more

In this

*Very Short Introduction*Richard Earl gives a sense of the more visual elements of topology (looking at surfaces)... more

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**The Rubik**less

**Don't have time to read the top Topology books of all time? Read Shortform summaries.**

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**AUTHOR**Chris McMullen earned his Ph.D. in particle physics from Oklahoma State University. Dr. McMullen currently teaches physics at Northwestern State University of Louisiana. His background on the geometry and physics of a possible fourth dimension of space includes a half-dozen research papers on the prospects of discovering large extra dimensions at the Large Hadron Collider.

**DESCRIPTION**This book takes you on a visual tour of a fourth dimension of space. It is much more visual and conceptual than algebraic, yet it is detailed and technical, with the intention of... more

**Don't have time to read the top Topology books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

The idea of algebraic topology is to translate problems in topology into problems in algebra with the hope that they have a better chance of solution. The translation process is usually carried out by means of the... more

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The opening chapter offers activities that explore the world of knots and links — including games with knots — and invites the reader to generate their own questions in knot theory. Subsequent chapters guide the reader to discover the formal... more

The authors begin with a brief review of the basic properties of the circle and related figures. They then show the many ways in which the circle manifests itself in the field of geometry--leading to some amazing relationships and truly important geometric theorems. In... more

**Don't have time to read the top Topology books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.