Algebraic Topology advice

Question

I'm currently working through Allen Hatcher's Book on algebraic topology and I'm noticing his sluggishness in style, I was wondering what other book on algebraic topology would work well alongside hatcher's book that helps make the ideas a bit more concrete and isn't as unorganized. Thus far I'm looking at Rotman's text for algebraic topology which I hear is excellent. There's also Fulton's text. I'm right now leaning toward obtaining rotman's text since it looks really good for a first run through of algebraic topology.

Answer 1

Try Tammo tom Dieck's Algebraic Topology. It is very detailed and a good supplement to Hatcher.

I'm learning the material myself, I follow Hatcher and for clarification and expansion of points I look up tom Dieck since it is so full of detail that it is easy to get lost in it.

Answer 2

There is also a really good lecture series by Dr. Jonathan Evans (here). It covers the basic topics in undergraduate algebraic topology finishing with the perhaps the highlight discussing the Galois correspondence for covering spaces.

Answer 3

I think James R. Munkres's Elements of Algebraic Topology is a great advice. It marches towards the central topic of homology theory straight ahead without the redundant mention of homotopy theory of topological spaces. It is organized very well, with rigorous foundations and a lot of concise examples that provides geometric intuitions and help to think. The proofs are written so well, too, that the reader can very easily capture the essential ideas, like the proof of simplicial approximation theorem.

Answer 4

I spent a considerable amount of time looking for the best algebraic topology for the graduate level. Among all of textbooks published by the end of 2022, I found Rotman's An Introduction to Algebraic Topology the best one.