"I would definitely recommend this book to a reader already acquainted with abelian varieties wishing to go beyond the basics of the subject. It is stimulatig and provocative and at the same time well-organized. Even the expert will learn a lot from reading it." Bulletin of the AMS
The aim of this book is to present a modern treatment of the theory of theta functions in the context of algebraic geometry. It starts with the classical theory of theta functions (in which the usual Fourier transform plays the prominent role), and then shows that in the algebraic approach to this theory (originally due to Mumford), the Fourier-Mukai transform can often be used to cast new light on many important theorems. Graduate students and researchers working in algebraic geometry will find much of interest in this volume.