I'm trying to read a document that applies Riemann-Roch left, right and center. I don't know this theorem or the theory it comes from so I need to build up a bit more background before I can tackle this.
Can you please recommend good books or (online) lecture notes which cover "multi-valued functions", Riemann Surfaces and similar up to (at least) Riemann-Roch? (I also want to pick up a bit about modular forms and the relation between lattices and elliptic curves).
(I've done a bit of complex calculus but it was all with analogy to real analysis so I am not sure that it will really give me any head start here. Also apologies for being so vauge with this but I don't know enough about this subject to be any more precise)