The gravitational million-body problem is a model for understanding the dynamics of rich star clusters. This text describes the theory astronomers need for studying globular star clusters. After introducing the million-body problem from various view-points, the book systematically develops the tools needed for studying the million-body problems in nature, and introduces the most important theoretical models. Written for graduate students and researchers in astrophysics and astronomy, this text also has important applications in the fields of theoretical physics, computational science and mathematics.