Books/Notes recommendation request: Multivalued functions/Riemann surfaces

The book by Otto Forster on Riemann Surfaces is pretty good. I never finished reading it myself, but it covers things like Riemann-Roch and Abel's theorem from a sheafish viewpoint. In particular, the proof of Riemann-Roch is analogous to the one in Hartshorne; it follows from the Serre duality theorem and an inductive argument. Learning about sheaves is definitely a plus.

Also, there's a book by Springer, though the level is a bit more elementary.