What are the most important graduate-level (sub)branches of mathematics and their prerequisites?

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As a self learner, sometimes I am really surprised when I find about a branch that I didn't know it existed, and only once I know about it, I find it everywhere and everyone seems to know it and that it's obviously important; the top example being Analysis, for quite some time I just thought it was another way of saying calculus. Another not-so 'obvious' example would be model theory, another representation theory (which I learned about yesterday).

I understand that this could be answered with thousands of topics but I want to know the 'main' ones if such a thing exists. Ideally, I'd like something like Teach Yourself Logic, or something with a structure similar to that. More simply, I'd be satisfied with just a nested list of branches (e.g. logic) and then some main subbranches (e.g. model theory, set theory, etc) under it with a short description of it.