Lectures notes on compact Riemann surfaces

Understand

This is an introduction to the geometry of compact Riemann surfaces, largely following the books Farkas-Kra, Fay, Mumford Tata lectures.

• 1) Defining Riemann surfaces with atlases of charts, and as locus of solutions of algebraic equations.
• 2) Space of meromorphic functions and forms, we classify them with the Newton polygon.
• 3) Abel map, the Jacobian and Theta functions.