A survey of modern techniques in the theoretical study of partial differential equations focusing on nonlinear equations. Includes treatments of the energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; and shock waves and entropy criteria for conservation laws. Intended for graduate students and research mathematicians. Annotation c. by Book News, Inc., Portland, Or.