Studying the dynamics of a large number of particles interacting through long-range forces, commonly referred to as the N-body problem , is a central aspect of many different branches of physics. In recent years, physicists have made significant advances in the development of fast N-body algorithms to deal efficiently with such complex problems. This book gives a thorough introduction to these so-called tree methods , setting out the basic principles and giving many practical examples of their use. The authors assume no prior specialist knowledge, and they illustrate the techniques throughout with reference to a broad range of applications. The book will be of great interest to graduate students and researchers working on the modeling of systems in astrophysics, plasma physics, nuclear and particle physics, condensed matter physics and materials science.