Physicists are conducting increasingly complex experiments in the hope of advancing our understanding of the universe. To fully exploit the discovery potential of these experiments it will be crucial to use optimal methods of data analysis. Since physical processes are generally characterized by many variables, optimal methods are necessarily multivariate, and neural networks are the most promising of them. These have the potential to revolutionize data exploration in high energy physics -- witness, as a recent example, the spectacular success with which neural networks have been used in top quark physics and searches for new particles.This book draws together the dispersed expertise of the scientific community to provide a unified, coherent and practical exposition of multivariate methods as they are (and will be) applied. It is a timely reference for high energy physicists and researchers in related fields who need a concise introduction to the subject. The first three chapters contain an exposition of the main concepts of multivariate methods, while the remaining chapters focus on applications using real examples. A convincing case is made that neural networks will be the method of choice in future analyses.