In 1919, Bieberbach posed a seemingly simple conjecture. That "simple" conjecture challenged mathematicians in complex analysis for the following 68 years! In that time, a huge number of papers discussing the conjecture and its related problems were inspired. Finally in 1984, de Branges completed the solution. In 1989, Professor Gong wrote and published a short book in Chinese, The Bieberbach Conjecture, outlining the history of the related problems and de Branges' proof. The present volume is the English translation of that Chinese edition with modifications by the author. In particular, he includes results related to several complex variables. Open problems and a large number of new mathematical results motivated by the Bieberbach conjecture are included. Completion of a standard oneyear graduate complex analysis course will prepare the reader for understanding the book. It would make a nice supplementary text for a topics course at the advanced undergraduate or graduate level. Titles in this series are copublished with International Press, Cambridge, MA. Readership Advanced undergraduates, graduate students, and research mathematicians interested in functions of a complex variable. Reviews "For those wanting to read about the history and resolution of what for many years was the problem in complex analysis, it should prove useful."  Bulletin of the LMS "This book (with a preface by Carol H. FitzGerald) is a concise, readable, and essentially selfcontained account of the mathematics that makes up the history of the Bieberbach conjecture."  Zentralblatt MATH Table of Contents  Introduction
 Löwner theory
 Grunsky inequality
 De Branges theorem
 Several complex variable cases
 References
 List of symbols
 Index
