*blocks your path*

Honestly point set topology is a major drag. Everyone should learn metric space topology by taking analysis, learn a tiny bit of general topology, and then move on to algebraic topology (and don't use Hatcher for God's sake).

what's wrong with hatcher? Alternatives?

Hatcher is just really poorly written. He rambles on and on, gives lousy proofs, and his treatment of cohomology makes me want to die. I mean, fuck, he even has objectively wrong sign conventions, resulting in a bunch of anticommuting squares. This is not something that should ever be published.

I recommend the Fomenko and Fuchs book on homotopical topology. (Despite the name, it's very much so a classical algebraic topology book.) Be careful, the two editions are quite different. And ignore the section on the ASS. If you've already learned some AT and just want a short book, May's Concise Course is a good pick (the sequel is not). Ignore the last chapters. However, you'll have to supplement with something for spectral sequences, which should be learned early. The previous book is good for this. There are other books good at other specific topics, but those are two good general ones.

what's your opinion on Bredon ?

I've heard it's nice and precise, but it's too (differential) geometric for my tastes. I find that people who learn co/homology from the De Rham viewpoint first have a hard time really grasping the nuances of cohomology in the sense of algebraic topology. Of course, if you're more interested in geometry, then it's probably a good book, but I've never looked at it too closely.

I have the choice of taking advanced PDE's or topology for my last class for my minor, is OP's book any good?

>Honestly point set topology is a major drag.
Don't listen to this fag, this is a horrible opinion of a pleb.
General topology and set theoretic topology are fucking rad.

>Honestly point set topology is a major drag.

It can be interesting if presented correctly. Look at Janich's Topology.

>Homotopical topology
Good taste user, fomenko in general has some nice books. There's a few other books that are good for these sorts of things, bott/tu is nice in that it approaches algebraic topology in a way that provides intuitive crunches for more abstract concepts. Tom dieck's is also good.
If you haven't taken measure theory and/or functional analysis than strauss is good, if you have than try evans, jost, or brezis, they each have their own styles so you'll have a pretty decent pick. If you want to learn topology munkres is standard though there are other books like janich that are very good.

At least study locales instead.

/r/ introductory text on pointless topology for someone with a background in Category Theory and Intuitionistic Logic but who doesn't give a single fuck about Algebra.

>pointless topology
sounds about right