Classical Topics in Complex Function Theory

This book is an ideal text for an advanced course in the theory of complex functions. The author successfully enables the reader to experience function theory personally and to participate in the work of the creative mathematician. Unlike the first volume, it contains numerous glimpses of the function theory of several complex variables emphasizing how autonomous this discipline has become. Covered are Weierstrass' product theorem, Mittag-Leffler's theorem, the Riemann mapping theorem, and Runge's theorems on approximations of analytic functions.

Remmert elegantly breaks the material down into small intelligible sections, with perfectly compact proofs and historical comments interwoven throughout the text. The abundance of examples, exercises, historical remarks (e.g. Gauss' review of Riemann's thesis), and an extensive list of references will make this book an invaluable source.