# Top Ten Math Books on Topology

There are many different math books to choose from when it comes to topology, or the study of shapes and topological spaces. Some may be even be downloaded for free on the Internet and can be found by doing a search for topology book PDF or topology books free download. For the top ten recommended topology books, check out the following list from Amazon’s math book section.

A First Course in Topology: An Introduction to Mathematical Thinking (Dover Books on Mathematics)

This introduction book is geared towards under-graduate students. It provides exercises for students to prove several theorems. It covers topological spaces and basic concepts along with product spaces and connectivity and additional subjects such as separation axioms and homotopy.

This is a good topology book that offers a great introduction for those who may have no prior knowledge concerning the subject of topology and is especially helpful to those who learn better with illustrations and visualization. People who seek to understand mathematics, especially concerning topology will be greatly helped by this “hands-on” book.

Introduction to Topology and Modern Analysis

Another book that gives an introduction to topography, it also strives to help its readers better understand the concepts of “continuity and linearity.” Some of the highlights of this book include theory of metric spaces and finite-dimensional spectral theory. While it covers many different topics, it is primarily an introduction to topology that covers every part of the subject matter.

A Mathematical Gift, 1: The Interplay Between Topology, Functions, Geometry, and Algebra (Mathematical World) (v. 1)

This book offers a way for students to learn about the serious subject of mathematics in a fun and engaging way. Even though it is primarily used for undergraduates in college, this book also allows for students in a high school setting to be introduced to the subject of topology. It has illustrations and straightforward explanations to complicated problems.

Topology of Gauge Fields and Condensed Matter

Even though this book is geared towards physicists and mathematicians, it has acquired a much larger audience thanks to its concisely written applications that discuss all the necessary theorems in order to understand the subject of topology.

The Shape of Space (Chapman & Hall/CRC Pure and Applied Mathematics)

This is also another good topology book that was written by a MacArthur Fellow who was a consultant to NASA on cosmological observations. While the book is pure mathematics, the topology concepts presented can be understood by high school students, including those who don’t even like math. This book seeks to answer questions like, “What shape is our universe?”

A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics Series)

This may be the best algebraic topology textbook on the market when it comes to students gaining an initial exposure to this particular subject matter. Written by a professor of mathematics at the University of Chicago, the book presents a complete discussion of developments in modern algebraic topology that have evolved over the last few decades while keeping in mind some of the historical theorems that have developed throughout time.

Euler’s Gem: The Polyhedron Formula and the Birth of Topology

Even those who have no prior knowledge of topology will enjoy this book which combines history and mathematics in a story-like fashion to explain one of math’s most important formulas. The book also contains examples, proofs and anecdotes that both students, teachers and professors at all levels will find engaging and wanting to learn more.

As one of the most recommended topology books, this second edition of *Topology* is an introduction that gives in-depth coverage of both general and algebraic topology. It is filled with clearly written concepts that allows someone to comprehend the material with or without an instructor. Students can even download solutions to exercises by searching for “topology Munkres solution manual pdf”

An Introduction to Algebraic Topology

Another book that focuses specifically on algebraic topology, this is considered the best algebraic topology book when it comes to getting an introduction to the subject. It covers basic concepts but it does assume the reader already knows about point set topology and basic algebra. The exercises allow the student to gain understand of the subject matter fairly easily.