The purpose of this book is to inform mathematicians about the applicability of graph theory to other areas of mathematics, from number theory, to linear algebra, knots, neural networks, and finance. This is achieved through a series of expository chapters, each devoted to a different field and written by an expert in that field. This book is more than a collection of essays however, in that the chapters have been carefully edited to ensure a common level ofexposition, with terminology and notation standardized as far as possible. This book will be useful to professsional mathematicians and graduate students. It should also appeal to scientists working in other areas.