Richard Montgomery is Professor Emeritus of Mathematics at University of California, Santa Cruz. He is a co-rediscoverer of the surprisingly stable figure eight orbit for the classical three-body problem. His work on the N-body problem uses variational, topological, and differential geometric methods to say new things about this old problem.

Part I. Tour, Problem, and Structures: -1. A tour of solutions; 0. The problem and its structure; Part II. The Questions: 1. Are the central configurations finite?; 2. Are there any stable periodic orbits?; 3. Is every braid realized?; 4. Does a scattered beam have a dense image?; Appendices: A. Geometric mechanics; B. Reduction and Poisson brackets; C. The three-body problem and the shape sphere; D. The orthogonal group and its Lie algebra; E. Braids, homotopy and homology; F. The Jacobi-Maupertuis metric; G. Regularizing binary collisions; H. One-degree of freedom and central scattering; References; Index.

"Examining the classical N-body problem, this book demonstrates that the field is still vibrant, exploring four of the big open questions. It describes the progress made, emphasizing open areas of research. For mathematicians, physicists, and astronomers curious about the N-body problem, this book presents the state of the art"--