Theory of Complex Functions

This is the english translation of a german textbook. Among its qualities are: very good order of subjects, a good synthesis of classical results and theorems, an open view on current research in the field, glimpses of functions of several complex variables and historical notes.This covers all the basic material needed for a graduate in mathematics preparing him/her to read the sequel: "Classical Topics in Complex Function Theory". Same author (with Grauert), same editor.My only regret is the relatively few exercices compared to other books, but this quite easy to find anyway in the litterature.Most quotations are both in the original language and translated.

This book is a beautiful look at classical complex analysis. At first glance it may look like it doesn't cover that much, but look carefully at the text. There are many great books on the subject, but this is one of the best. For example, I love Alhfors, but it is a bit dry. This book however, is not dry at all.