The goal of the course is to learn about compact Riemann Surfaces. The main topics will be: Differential forms and their integration, Dolbeult lemma, DeRham-Dolbeult's Theorem, Cohomology groups of line bundles, Meromorphic functions, Riemann-Roch Theorem, Serre Duality Theorem, Abel-Jacoby Theory.
All the necessary information can be found here
A first course in Topology might help.