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 comfortable with the book

Geometry of Algebraic Curves by authors Harris, Arbarello,Griffiths,Cornalbla