This book systematically develops methods for proving the non-vanishing of certain L-functions at points in the critical strip. Researchers in number theory, graduate students who wish to enter the area, and non-specialists seeking an introduction to the subject will benefit from studying this book. One of the most attractive features of the monograph is that it begins at a very basic level and quickly develops enough aspects of the theory to bring the reader to a point where the latest discoveries presented in the final chapters can be fully appreciated. This book has been awarded the Ferran Sunyer I Balaguer 1996 prize. The deepest results are contained in Chapter 6 on quadratic twists of modular L-functions with connections to the Birch-Swinnerton-Dyer conjecture. It is well-suited and stimulating for the graduate level.