I am a master's student planning to write master's thesis in riemann surfaces.I plan to study forster's riemann surfaces.What side topics could one study to spice up the thesis.I am particularly interested in analytic aspects.

Added later..
Could anyone suggest ho much background would one require to understand geometry of algebraic curves by harris,arbarello,etc... i know already complex algebraic curves of Kirwan except the last chapter on singular curves. Which books would provide me enough materials so that I can start feeling with that book.