This volume of Surveys in Differential Geometry is dedicated to the three most eminent contributors to the subject of regularity and existence of nonlinear partial differential equations, which has played such an important role in geometry. These are Richard Hamilton, Leon Simon, and Karen Uhlenbeck. Presented topics include: analysis related to minimal submanifolds, Yang-Mills theory, Kähler metrics, Monge-Ampère equations, curve flows, and general relativity.