TITLE: Learning Roadmap for Algebraic Topology
QUESTION [67 upvotes]: I am now considering about studying algebraic topology. There are a lot of books about it, and I want to choose the most comprehensive book among them.
I have a solid background in Abstract Algebra, and also have knowledge on Homological Algebra(in fact I am now study Tor and Ext functors). But my knowledge in topology is poor, very poor. I could only remember the concepts, but I got no idea with problems.
Please feel freely suggesting me some book to work on.
Thank for reading.

REPLY [11 votes]: Firstly, let me qualify this answer by acknowledging that I don't know algebraic topology very well and have only assimilated the rudiments of homotopy and homology theory. That being said, I find the two texts by Prosolov, Elements of Combinatorial And Differential Topology and Elements of Homology Theory, to be very promising. These texts are meant to be read sequentially and each text introduces problems in a just-in-time fashion and to which hints and, in many cases, full solutions, are provided. This feature makes these texts very suitable for self-study and is a rarity among algebraic topology texts. The author doesn't expect you to have a thorough background in differential geometry and introduces these concepts as needed. Although in the first volume he does cover basic definitions from point set topology, you will probably need to supplement it with a good general topology text as others have suggested, e.g., Munkres.