Resources for self-study of general topology Could you point me to good resources for self-study of general topology. I want to learn the basics and how to prove theorems about structures like polyhedra by myself.
A great resource for self-study in Topology is James Munkres' Topology. You can "preview" the text and it contents at the link given. It's divided into two sections, the second being algebraic topology. 

You'll also get an overview of Topology (Wikipedia), its branches and the topics related to those branches/subfields, to better hone in on your area of interest. There are a number of references cited, some with links, along with helpful resources that may aid in your self-study.

A good follow-up to Munkres, and more in the direction of your interests, I presume, is then (of course) Algebraic Topology by Allen Hatcher (freely and legally available online, courtesy of the author! The link takes you to Hatcher's home page, where you can access his text, as well as supplementary resources, e.g. notes in point-set-topology.) You might want to peruse Hatcher's text to get a better idea what preliminary material you should cover in Munkres; that might cut down on the amount of Munkres you'd want to cover.

Another sound intro to Topology is A First Course in Topology by J. McCleary (again, you can preview the text at the given link).
Introduction to Topology: Third Edition (Dover Books on Mathematics) Bert Mendelson