Riemann Sphere/Surfaces Pre-Requisites

Question

I have recently developed a large interest in everything to do with Riemann Sphere/Surfaces. I wish to understand the topic quite well but I know that I will need to read a good number of books on topology and complex and real analysis.

Can you recommend any good books that will allow me to move onto Riemann Surfaces? I am theoretical physics student so my knowledge in maths isn't as detailed as that of a typical maths student, but I'm not letting that stop me.

Thanks.

Answer 1

try

J. Jost Compact Riemann Surfaces, third edition Springer Universitext. (I think is a very good book) http://www.zbmath.org/?q=an:05044797

and

S. Donaldson Riemann Surfaces. (this is beautiful but it is more "concentrated") http://www.zbmath.org/?q=an:05900831

Also you may find interesting this fantastic book about topology of manifolds.

Milnor, Topology from a differential viewpoint. http://www.zbmath.org/?q=an:01950480

Answer 2

Have a look at the following video lectures

http://nptel.ac.in/courses/111106044/

I don't know about your background but perhaps one of the best book on Riemann Surfaces is Algebraic Curves and Riemann Surfaces by Prof. Rick Miranda. You can also have a look at the following notes

https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CCYQFjAA&url=http%3A%2F%2Fmath.berkeley.edu%2F~teleman%2Fmath%2FRiemann.pdf&ei=P-wnU6jgMcXqrAf-nYGQDg&usg=AFQjCNH3cJVuhParKyo9Fpw9utGgswrkhQ&bvm=bv.62922401,d.bmk