An Introduction to Algebraic Topology (Graduate Texts in Mathematics, 119) First Edition

As a student approaching the subject, this book was just the right pace to self-study. When learning high level subjects from a book, I enjoy simple exercises requiring basic understanding and memory of theorems. Sure the exercises are too easy to be "homework problems", but they're nice for cementing the material, and it's possible to read the book and solve all of them in a few weeks (maybe less if motivated).

From years of experience there is no perfect book on the subject. However there are 4 books, mixing them together gives a good flavour of the subject. The first two are Rotmans and Hatchers books ,and supplemented by Massey and with the right maturity, Spanier’s . Among the four I Recommend Rotman’s as a start.

very friendly introduction in algebraic topology suitable for self-study. A lot of details are given. The exercises are simple applications of the theory developed in the text.

This is great as a first algebraic topology book. He writes very clearly and provides ample details for those unfamiliar with abstract nonsense. Those already familiar with diagram chasing will probably want to skip the thoroughly explained diagram chases. My only complaint is that the exercises are too easy. Most of them are definition pushing and routine verifications. I do think that such exercises are necessary to become familiar with the basic definitions and notions. However, it is only after slaving over some challenging problems for a few hours that the student is able to fully assimilate the material. That being said, this book would be ideal to accompany a course.

I'm using the book mostly for self-study and have found it very useful. I also have Hatcher's book, which has fantastic examples and pictures, but I prefer Rotman's style for definitions and results. Rotman takes the time to carefully develop the notions of category theory so that definitions and results can be couched in this language.

Each text that I have read by Rotman is logically sound, well thought out, there are ample explanations, exercises as well as examples, and moreover, Rotman does an excellent job proving results. Sure he leaves the reader to prove certain results but, in general, all major concepts he will prove or, when it comes to familiar sticking points for students, Rotman will show that reader how to effectively prove these types of results. Now, Algebraic Topology is not an easy subject (actually it is a beautiful and far-reaching subject) and, depending upon the authors approach, the level of 'mathematical' maturity required can quickly escalate. Rotman's text is just above middle of the road with respect to this proverbial and undefined notion-'mathematical maturity'. Not as far-off as Spanier and not quite as gentle as Hatcher. For the reader who has this maturity or the necessary background, then Rotman's text is a must read provided you enjoy texts that follow the theorem-proof-theorem format. Furthermore, the logical consistecny with respect to how and when material is present to the reader places this text in a league of it's own. Without a doubt I could imagine any beginning graduate student or confident undergradute tackling this text on their own. For example, I am no math wizard but with only a background consisting of point-set topology with an introduction to the Fundamental Group, Abstract Algebra (Hungerford style) and Analysis (Rudin style) I was able to begin reading and, in particular, solving problems from Rotman's text while a senior undergraduate. For those of you who would like to learn the subject and learn it well but who are scared of this text (Springer can do that to people) I wouls strongly recommend pairing this text with Allen Hatchers or Part II of James Munkres' text depending on your level of enjoyment with respect to suffering your way through texts. In fact, I would suggest reading Munkres in its entirety since, this approach would properly prepare your for Rotman's text and the transition would be seamless. Finally, if, while reading this text you find yourself feeling lost during the initial chapters due to the use of Category Theory, I would suggest pushing forward and not becoming too hung up on acquirring a 'total' understanding. Things will make more sense as you progress through the later chapters. Enjoy and good luck!5 April 2011 - Updated to 5 stars: I must have fell asleep at the wheel when aiming for the stars.

It seems Allen Hatcher book is going to be the standard in ATI strongly feel ¡¡ What a pity¡¡The Rotman books is much much clearer and better, then my advice isIf you can afford the cost give up Hatcher's and get Rotman's

Very good