I'm trying to go through Allen Hatcher's Algebraic Topology book: https://pi.math.cornell.edu/~hatcher/AT/AT.pdf
But the "introduction" lost me completely. By someone's recommendation I skipped chapter 0 and drove right into chap 1, but I found that his style does not resonate with me. I don't think its very rigorously organized or pedantic.
I am acquainted with de-Rham Cohomology, but I don't know what a cohomology in general is.
I tried looking at Tammo tom Dieck's book: https://www.maths.ed.ac.uk/~v1ranick/papers/diecktop.pdf
But I read that his book is a great supplement to Hatcher, which suggests it is not good as a primary source.
I looked at Rotman's book: http://www.ugr.es/~acegarra/Rotman.pdf
I think it looks great, and from what I've seen as I skimmed through, it is in a style that I would appreciate. But my concern is that it might be outdated or it does not cover a lot of the subject.
Should I just persevere with Hatcher? Or are there other free books on algebraic topology. I'm looking for a rigorous and broad coverage of the subject.