In spite of being nearly 500 years old, the subject of complexanalysis is still today a vital and active part of mathematics. Thereare important applications in physics, engineering, and other aspects oftechnology.This Handbook presents contributed chapters by prominentmathematicians, including the new generation of researchers. More than acompilation of recent results, this book offers students an essentialstepping-stone to gain an entry into the research life of complexanalysis. Classes and seminars play a role in this process. More,though, is needed for further study. This Handbook will play that role.This book is also a reference and a source of inspiration for moreseasoned mathematicians—both specialists in complex analysis and otherswho want to acquaint themselves with current modes of thought.The chapters in this volume are authored by leading experts andgifted expositors. They are carefully crafted presentations of diverseaspects of the field, formulated for a broad and diverse audience. Thisvolume is a touchstone for current ideas in the broadly construedsubject area of complex analysis. It should enrich the literature andpoint in some new directions.