[Math] learn the basics of cohomology


I am fishing for a textbook on basic Algebraic Topology. Almost every where I looked, I saw praises for Hatcher's textbook. Now, I already know a little bit of Homology (at the level of Munkres' Elements of Algebraic Topology), but looking at Hatcher's chapter on Homology I realized that I wouldn't have been able to learn much from it. For a lack of a better phrase, it would have appeared too hand-wavy for someone like me (due to my lack of mathematical maturity).

So, my question is where (apart from Munkres, preferably online) do I turn to learn the basics of Cohomology (say, at the level of Hatcher's chapter 3)?

PS: And, since I am a poor student, online lecture notes would be great.


Thanks everyone. But, I should have stressed that I am looking for lecture notes or textbooks that are freely available online. So I'll wait a bit more before accepting.

@Theo Buehler: Massey looks great. Thanks a lot. Unfortunately, I do not have access to my univ library over the summer. But, if I don't find any notes etc. then I'll accept your answer if you post it.

Best Answer

Firstly, I think that Munkres is excellent. But I also agree that Hatcher's is less accessible than Munkres. In addition to the excellent comments above (Theo's recommendation of Massey, even though expensive, is great - and if you are a student with access to a math library, I bet it will be there).

But I point you to the Autodidact's Guide, something published in Notices of the AMS a while back. It recommends different books for almost every subject, and their topology section is right on.