I am a master's student planning to write a master's thesis on Riemann surfaces. I plan to study Forster's *Lectures on 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 how much background would one require to understand geometry of algebraic curves by authors such as Harris, Arbarello, etc... I know already *Complex algebraic curves* by Kirwan, except for the last chapter on singular curves. Which books would provide me enough materials so that I can start feeling with that book.