Approaching the Riemann-Roch Theorem for algebraic curves

Question

I am using "Algebraic Curves: An Introduction to Algebraic Geometry" by William Fulton as a guidline for approaching the Riemann-Roch Theorem for algebraic curves. I have two questions:

1. What chapters of the book should I go through in order to fully understand and prove the theorem? Or, is all of it necessary?
2. Is there any other source that you would recommend for approaching the theorem?

I should also mention that I am a postgraduate student.

Thanks in advance!