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Topology is a complicated yet informative brand of math. It uses thereoms, formulations, and proofs. Topology is the study of geometric properties and shapes. This branch of math is very similiar to geometry, but it is much more complex. Topology is an advanced level of math that is often studied at the undergraduate or graduate levels. Those majoring in math definitely have to learn it. Those studying engineering or physics do, too. The concept is complicated, but necessary in life. Students looking to get an edge on school can do some of their own research on topology.
What are the Best Topology Books to read?
The books listed below have a lot of great information on topology and what it is. The books have all kinds of angles and they tackle topology from their own interesting angles. Topology can be boring. With the right book, readers won’t think so. They’ll love reading about topology.
Best Books on Topology: Our Top 20 Picks
Here are some of the best topology books that you can consider to expand your knowledge on the subject:
Topology by James R. Munkres is a simple, straight-foward book on the topic of topology. Topology is the study of spatial relations and geometric properties, or rather as change in shapes and sizes. Munkres helps those who love math take their education to a whole new level.
This book is great for both high school level students as well as college level students. It uses simple language and it is easy to teach. A variety of topics are discussed in it, as well. Some of these topics are: theory and logic, topological spaces, metrization theorems, the fundamental group, and more. This is a basic introduction to topology, and a book that truly makes sense of a complicated idea.
- Authors: James R. Munkres (Author)
- Publisher: Pearson (January 7, 2000)
- Pages: 537 pages
2. Introduction to Topology
Topology is a complicated math that can be difficult to understand. Introduction to Topology by Bert Mendelson is an instructive guide to topology. This is a great guide for beginners learning topology because it is very easy to read. It is also fun. The book includes examples, plenty of imaginative exercises, and it is very hands on. Readers will learn how they can use topology visually and physically.
Mendelson wrote this book with undergraduate students in mind. Mendelson wrote the book with simple language that is easy to study. He organized the chapters well, used lots of keywords, and made topology easy to learn. Professors will love teaching their students this book. It is straight to the point, and helps their students understand the math quickly. This is a wonderful book for learning topology.
- Authors: Bert Mendelson (Author)
- Publisher: Dover Publications; Third Edition (July 1, 1990)
- Pages: 224 pages
3. Team Topologies: Organizing Business and Technology Teams for Fast Flow
Team Topologies: Organizing Business and Technology Teams for Fast Flow by Matthew Skelton and Manuel Pais helps teams build up their topology game. The book will help readers discover team patterns that other companies use for success, how to evolve effectively as a team, how to split software, how to align teams, and many common team patterns.
The main focus of this book is using topology in a group, instead of as an individual. These ideas help readers and teams structure how to organize, study, and appropriately use topology to their advantage. Many people will enjoy this read, but particularly for companies who frequently use topology in a group setting. This is a book best for people with an advanced knowledge on topology.
- Authors: Matthew Skelton (Author), Manuel Pais (Author), Ruth Malan (Foreword)
- Publisher: IT Revolution Press; Illustrated Edition (September 17, 2019)
- Pages: 240 pages
4. The Pushing Points Topology Workbook
Topology is a great topic to read about, but it is easier to learn with physical learning and exercises. The Pushing Points Topology Workbook by William C. Vaughn is a software guide for SubDtopology. The book doesn’t talk so much about topology, as it uses topology exercises. There are as many as sixty exercises included in its pages. Each exercise has tips and tricks for implementing their techniques.
This book has many wireframe assets, as well as reference points for studying topology. It teaches the foundation of SubDtopology so readers can make anything with the program. It is really easy to understand, as well. It guides readers with step by step instructions that are easy to follow, informative, and interesting. This is a great read for all ages and levels.
- Authors: William C Vaughan (Author)
- Publisher: CreateSpace Independent Publishing Platform (April 5, 2018)
- Pages: 138 pages
5. Algebraic Topology
Algebraic Topology by Allen Hatcher is the first edition of this book. The book is one of four books necessary for first year undergraduates pursuing a degree in math. Algebraic topology is an essential subject when pursuing an advanced degree in math related fields. There is a broad range of topics included in this text. It uses research, examples, and exercises to explain topology. The book itself has four main chapters that help cover every bit of algebraic topology. These chapters are: fundamental group and covering space, higher homotopy groups, homology and cohomology, and homotopy theory.
Additionally, it covers a number of theorems. Even though this book has a lot of great information, reading it can be dull and boring. The information is not very exciting. It is hard to get through it. Those who aren’t interested in this topic should skip this Algebraic Topology for now. Those who get excited about topology, though, will really enjoy it.
- Authors: Allen Hatcher (Author)
- Publisher: Cambridge University Press; 1st Edition (October 29, 2009)
- Pages: 556 pages
6. Counterexamples in Topology
Topology is difficult to read about. Examples help explain this difficult concept. Counterexamples in Topology by Lynn Arthur Steen and Arthur Steebach Jr. is a book full of topology examples that help mathematicians understand topology, and use it in life. There are over 140 interesting and exciting examples included in this book. Some of the visuals the Counterexamples in Topology uses are charts, venn diagrams, and more to explain topology. Not only does the book have examples, but it also includes problems that can be addressed and fixed with these examples.
This book is compact and straight to the point. It is well-organized, easy to read, and great for mathematicians of all levels. It is particularly beneficial to readers who are testing a conjecture that are having a difficult time proving. There is plenty of great information on topology and so many wonderful examples included in this read.
- Authors: Lynn Arthur Steen (Author), J. Arthur Seebach Jr. (Author)
- Publisher: Dover Publications; New edition (September 22, 1995)
- Pages: 272 pages
7. General Topology
General Topology by Stephen Willard is a great book for math experts of all levels. Students in high school, undergraduate, and graduate schools can all gain something from this book. This book discusses topology in general. It explains what it is, how to use it, and how it compares to other kinds of math. Willard discusses the two areas of topology: continuous topology and geometric topology. Continuous topology is the topology that uses convergence, metrization and compactness.
Geometric topology is covered by nine sections that detail homotopy theory, connectivity properties, and topological theorems. The book also has plenty of historical notes that adds a new layer to topology. It explains topological theories well and gives students and teachers a better understanding of topology and geometry. This is a topology text for everyone.
- Authors: Stephen Willard (Author)
- Publisher: Dover Publications; Illustrated Edition (February 27, 2004)
- Pages: 384 pages
8. Differential Topology
There are many types of topology. Differential topology studies the structures of manifolds and property structures. Differential Topology by Victor Guillemin and Alan Pollack is an elementary guide to the study of smooth manifolds. Guillemin’s book is considered a mathematical masterpiece.
This book has many many exercises that will help readers understand differential topology and implement it. Its contents gives readers step to step guides on differential topology and on how to use it. That being said, this book has a lot of flaws and faults. Some of those faults are in the grammar, and others are in the math. The structure of the book reads like a novel. This could be considered a good or bad thing depending on the reader. It is, however, easy to read and very informative.
- Authors: Victor Guillemin (Author), Alan Pollack (Author)
- Publisher: American Mathematical Society; Reprint Edition (August 16, 2010)
- Pages: 222 pages
9. Introduction to Topology
Introduction to Toology by Theodore W. Gamelin and Robert Everist Greene is in its second edition. This book is a little different than other topology books. Within the first two chapters it addresses metric spaces and point-set topology. Later in the book, algebraic topological material is addressed. The structure of this book follows the authors’ thought process. Gamelin and Greene create an incredible introduction to topology. It is easy to understand, and was written to help readers easily understand the knowledge.
This book is a great for beginners in the topic of topology because it addresses their frequently asked questions. However, it only scrapes the surface of topology. It does not go too into depth, nor does it explain complicated theories. It is a great book for beginners, but not for those with more experience.
- Authors: Theodore W. Gamelin (Author), Robert Everist Greene (Author)
- Publisher: Dover Publications; Second Edition (February 16, 1999)
- Pages: 256 pages
10. Basic Topology
Many undergraduate students study math or majors that are related to math. Basic Topology by M.A. Armstrong is the perfect book for those students. Students love a book that is easy to read and provides lots of research and examples. They can read this book in their spare time, but it also might be listed as one of their textbooks. Professors can easily teach their students these topics because of the way M.A. Armstrong wrote the book. It is well-organized, simple, and includes many exercises.
The book has illustrations of theorems that help the readers better understand the information. Armstrong did a great job of making a basic text that will help students increase their knowledge on topology, and move forward with their math degrees.
- Authors: M.A. Armstrong (Author)
- Publisher: Springer; Binding Damaged and Torn Edition (May 1, 1997)
- Pages: 251 pages
11. Topology from the Differentiable Viewpoint
Topology from the Differentiable Viewpoint by John Willard Milnor is a concise introduction to topology and all that is related to it. Milnor himself is a brilliant mathematician, so this book is backed by reasoning and his own research.
The book begins by discussing basic concepts, and continues by diving into intricate theories. It then discusses concepts like: tangent spaces, vector fields, oriented manifolds, and more. This text also delves into Sard’s and Hopf’s theorem. Milnor discusses these theories, and also provides proofs of them. This is definitely a theorem based book that will intrigue readers and engage them. It is also a great accompaniment to videos on topology online. This book is a great contribution to combining print and digital mediums.
- Authors: John Willard Milnor (Author)
- Publisher: Princeton University Press; Rev ed. Edition (November 24, 1997)
- Pages: 80 pages
12. Essential Topology
Topology is an important mathematical topic. Essential Topology by Martin D. Crossley explains just why that is. It unites modern topology with plenty of topology and math research. The book helps readers and students self study. Even if this book isn’t used for a math class, students can still learn a lot from it on their own. This way they will be over-prepared for future math classes.
This is aninteresting read with a lot of great examples, but these examples can be redundant and repetitive at times. They can be boring and dull, but they are still great for visual learning. This book is informative, but there are a few minor and miniscule errors in it that affect the quality of the book’s contents.
- Authors: Martin D. Crossley (Author)
- Publisher: Springer; 1st ed. 2005. Corr. print 2010. Edition (July 1, 2005)
- Pages: 224 pages
13. A Concise Course in Algebraic Topology
A Concise Course in Algebraic Topology by J.P.P May is smart, and witty. It is a book that is clear cut and great for those who are learning about topology. This book reads like an informative class. Students can learn about topology just by reading this book. Teachers can use this book to teach their topology classes. It is super informative and interesting. Algebraic topology is part of everyday math. It is important to understand, especially for those who are studying math or a math related field.
This book is particularly great for advanced grad students. It provides quality information that experts in the field of topology can learn about. Beginner or intermediate mathematicians should put this on their reading lists for when they have studied math for a little while longer.
- Authors: J. P. May (Author)
- Publisher: University of Chicago Press; 1st Edition (September 1, 1999)
- Pages: 254 pages
14. Topology and Geometry
Topology and geometry are very similar math subjects. Topology and Geometry by Glen E. Bredon explains both subjects, their similarities, and their differences. This book discusses a number of theories, like homology theory and homotopy theory. The background on alegbra is a main theme in this text, too. It helps readers analyze math and use exercises to learn the subjects.
This book is clear and concise. It provides a straight-forward introduction to topology, geometry and some much more. It is smart and interesting. Math lovers of all levels will enjoy this book because of the wide range of information it includes. It is straight to the point, and it doesn’t drag on for too long. This text is the perfect length and a great read.
- Authors: Glen E. Bredon (Author)
- Publisher: Springer; Corrected Edition (October 17, 1997)
- Pages: 557 pages
15. Introduction to Topology
Introduction to Topology by Crump W. Baker is the perfect book for a college course on topology. Readers with varying degrees of math knowledge will enjoy this text. The book structures the content so students can learn the easy stuff first, and the more difficult stuff later. This way, if students have a lower level of math experience, they won’t lag behind. Reader can expect to use this book for undergraduate math courses, but it can also be used for advanced math classes.
The book starts out with sets and functions, and then leads to topological space. The book continues to cover a variety of topics. In chapter three, readers learn subspaces, homeomorphisms, and continuity. This is a great read for those who are just getting started with topology.
- Authors: Crump W. Baker (Author)
- Publisher: Krieger Pub Co (June 1, 1997)
- Pages: 155 pages
16. Elementary Applied Topology
Introductions to topology are important for explaining new and old mathematical theorems. One of these introductions is Elementary Applied Topology by Robert Ghrist. This book is engaging and interesting. It is basic, yet informative. Readers don’t have to be mathematicians to understand and enjoy this book. There are many theories included in this text. Some of these are: morse theory, sheaf theory, and more.
The elementary guide includes many tools and topics that help readers understand topology and understand complex math concepts. It is quite refreshing and is a unique topology read. That being said, some of the information in this book is not totally accurate, but overall it’s great. It has many diagrams and exercises that help readers visualize what they are learning.
- Authors: Robert Ghrist (Author)
- Publisher: CreateSpace Independent Publishing Platform; 1st Edition (September 1, 2014)
- Pages: 276 pages
17. Introduction to Topology: Pure and Applied
Topology is a hard concept to understand. Introduction to Topology: Pure and Applied by Colin Adams and Robert Franzosa is a book on the basics of topology. Elements of this book apply topology to the real world. The book helps readers understand topology through discipline and research. It covers a number of topics and applies topology to all kinds to situations, like: population modeling, heart stimulation, cosmology, DNA, and computer graphics. Adams and Franzosa also use this text to discuss many theories.
The theories they cover are: knot theory, degree theory, graph theory, dynamical systems and chaos, metric spaces, connectedness, and compactness. This book covers everything. However, it is definitely a book for beginners. Those with prior topology experience will find the book redundant, and a little too basic for their experience. This book is long and rigorous, but it has lots of quality information.
- Authors: Colin Adams (Author), Robert Franzosa (Author)
- Publisher: Pearson; 1st Edition (June 18, 2007)
- Pages: 512 pages
18. General Topology
General Topology by John L. Kelly is a clear cut book that defines what topology is, and different ways to use it. The book is perfect for professors who are teaching graduate level topology classes. It is also a great book for those who wish to improve their topology on their own. Mathematicians who are trying to self- teach themselves will love this work. The text has a background for modern analysis. It applies topology to life today. It explains problems and solutions in topology, as well as exercises and theorems.
This is a worthwhile book for topology lovers and math experts. It provides plenty of mathematical foundations for students. It helps them understand topology in an easy and interesting way. This book has all kinds of details on topology and math.
- Authors: John L. Kelley (Author)
- Publisher: Dover Publications; Reprint Edition (March 17, 2017)
- Pages: 320 pages
19. Principles of Topology
Topology is an important branch of mathematics. It is an interesting read on a complicated concept that all mathematicians should learn. Principles of Topology by Fred H. Croom discusses the main principles that make up topology. This is a great introduction to topology for undergraduate and graduate students. This guide has many topics.
Some of the book’s best topics are: general topological spaces, metric spaces, subbasis, connectedness, metrization, and product spaces. Historical notes are in this text, to. That is not a common theme in topological books. There are many exercises in this book that tests the students mathematical knowledge. All the major topics of topology are covered. This is a great book for professors teaching topology.
- Authors: Fred H. Croom (Author)
- Publisher: Dover Publications; First Edition, First (February 17, 2016)
- Pages: 336 pages
20. Elementary Topology
Elementary Topology by O. Ya. Viro, O. A. Ivanov, N. Yu Netsvetav, and V. M. Kharlamov is a textbook that covers all the basics on topology. This book has a quality introduction to topology, and it also includes an introduction to algebraic topology introduction. There are many theorems as well as proofs of them in this book. The contents of this text helps readers work actively with activities and examples. The authors organized it in an odd, but interesting way.
The book’s formulations and proofs are separated. This way, readers can focus on the formulations without being distracted by their proofs. They can try to come up with their own proofs, and compare them later. This is the perfect introduction to topology to mathematicians with all kinds of experience and interests. It is concise, interesting, and straight to the point.
- Authors: O. Ya. Viro (Author), O. A. Ivanov (Author), N. Yu. Netsvetaev (Author), and V. M. Kharlamov (Author)
- Publisher: American Mathematical Society (September 17, 2008)
- Pages: 400 pages
Choosing the Best Topology Books
These are some of many books on topology. They explain all kinds of information on the topic, as well as theories, exercises, and more. They help students understand this complex branch of math. After reading these books, they’ll consider topology easy. These texts help readers grasp a better understanding of all kinds of math, but especially topology. They are not too difficult to read and they are great for mathematicians.