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Learning Roadmap for Algebraic Topology

The title of the question already says it all but I would like to add that I would really like the book to be about more algebraic topology than its applications : it should contain theorems' proofs. Just adding that I have never taken a course on algebraic topology, I'm a bachelor student, so a "beginner" book style will be very good!!! Also mentioning what would be the prerequisites for mastering the branch is appreciated. Thanks.

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marked as duplicate by t.b., Byron Schmuland, lhf, Asaf Karagila, robjohn Dec 29 '11 at 18:56

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hatcher is readable and free online – yoyo Dec 29 '11 at 17:49
see also:… – t.b. Dec 29 '11 at 18:02

2 Answers 2

My first exposure to algebraic topology was Massey, followed by Hatcher, Rotman and May. I'm now studying Spanier and Dieck. You'll probably want to supplement these with good books in Homological Algebra and Category Theory. As for prerequisites, you'll need a good background in Point-Set Topology.

This bibliography contains most if not all of the good books in algebraic topology at various levels, as well as a nice collection of important articles in the field.

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A very good book is J. Frank Adams, Algebraic Topology, a student's guide.

But I started learning Algebraic Topology using the book Topolgy by JAMES R. MUNKRES. I think this is good for beginners because it was good for me as a beginner.

You might also consider Algebraic Topology by Allen Hatcher.

For prequisite, you will need Point-set topology and I strongly recommend Topology by James R. Munkres or Topology without Tears by Sidney A. Morris.

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