In spite of being nearly 500 years old, the subject of complex analysis is still today a vital and active part of mathematics. There are important applications in physics, engineering, and other aspects of technology. This Handbook presents contributed chapters by several of prominent mathematicians, including the new generation of researchers. More though than a compilation of recent results, this book offers students an essential stepping-stone for students to gain an entry into the research life of complex analysis. 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 more seasoned mathematicians--both specialists in complex analysis and others who want to acquaint themselves with current modes of thought. The chapters in this volume are authored by leading experts in the field, also gifted expositors. They are carefully crafted presentations of diverse aspects of the field, formulate for a broad and diverse audience. The Editors intends this volume is a touchstone for current ideas in the broadly construed subject area of complex analysis. It should enrich the literature and point in some new directions.