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.

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    $\begingroup$ Just a heads up, chapter 0 is 1000x more annoying than the other chapters. $\endgroup$ – mathworker21 May 2 '17 at 1:23
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    $\begingroup$ I really enjoyed (and continue to enjoy) Rotman's book. I think he does a great job separating the algebra and the topology, which helped my organize the ideas better in my head. For instance, in Ch. 10 he proves results about transitive group actions in the abstract, and then applies these to the case of the fundamental group acting on a fiber. $\endgroup$ – André 3000 May 2 '17 at 1:39
  • $\begingroup$ I am not a fan of Hatcher, but then I learnt the theory before it appeared. I like Marvin Greenberg: Algebraic Topology, also Bredon: Topology and Geometry, Munkres Algebraic Topology. Finally the book by Dold:Lectures on Algebraic Topology is great, lots of good material there, not sure if its an introductory book though. $\endgroup$ – Rene Schipperus May 2 '17 at 1:56
  • $\begingroup$ Rotman's book is rather long and he indicates many algebra and category than necessary . But anyway I usually find proof in his book and Hatcher's book along with Massey's book . $\endgroup$ – Gankedbymom Jun 3 '17 at 6:01

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.

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    $\begingroup$ Not to mention tom Dieck's book is endorsed by Hatcher himself!. :) $\endgroup$ – André 3000 May 2 '17 at 1:35
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    $\begingroup$ @Quasicoherent Hatcher's idea is fantastic. Some one should make a epub/pdf where clicking/tapping on sections expand into more detail or a site, this is just a few lines of javascript. $\endgroup$ – sntx May 2 '17 at 1:39

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