The second edition of the Handbook of Discrete and Computational Geometry is a thoroughly revised version of the bestselling first edition. With the addition of 500 pages and 14 new chapters covering topics such as geometric graphs, collision detection, clustering, applications of computational geometry, and statistical applications, this is a significant update. This edition includes expanded coverage on the topics of mesh generation in two and three dimensions, aspect graphs, center points, and probabilistic roadmap algorithms. It also features new results on solutions of the Kepler conjecture, and honeycomb conjecture, new bounds on K sets, and new results on face numbers of polytopes.