Covers the classical theory of abstract Riemann surfaces. This book presents the requisite function theory and topology for Riemann surfaces. It also covers differentials and uniformization. For compact Riemann surfaces, it features topics such as divisors, Weierstrass points, and the Riemann-Roch theorem.
This well-known book is a self-contained treatment of the classical theory of abstract Riemann surfaces. The first five chapters cover the requisite function theory and topology for Riemann surfaces. The second five chapters cover differentials and uniformization. For compact Riemann surfaces, there are clear treatments of divisors, Weierstrass points, the Riemann-Roch theorem and other important topics. Springer's book is an excellent text for an introductory course on Riemann surfaces. It includes exercises after each chapter and is illustrated with a beautiful set of figures.