Robert C. Gunning
Professor of Mathematics
Princeton University

Click here to download Function Theory of Compact Riemann Surfaces:

June 10, 2007; revised and extended August 12, 2008

This is a leisurely survey of compact Riemann surfaces from the point of view of function theory. It combines material from graduate lectures I have given on this topic over a number of years; some earlier lectures had been published in other forms but have been reworked and considerably extended for inclusion here, while the rest of the material is from more recent lectures. The book is a work in progress. Included here are those chapters that are in fairly final form; the table of contents lists other chapters that are still being revised or written, to be added eventually. I would greatly appreciate any corrections or suggestions that readers would care to send on to me.