These notes, based on the classic lectures Lax (Courant Institute of Mathematical Sciences) delivered at Stanford U. in 1963, include basic theory and descriptions of finite approximations of hyperbolic equations. Lax starts with the basic notions, then describes the finite speed of the propagation of signals references, hyperbolic equations with variable coefficients, pseudodifferential operators and energy inequalities references, the existence of solutions, waves and rays, finite difference approximation to hyperbolic equations, scattering theory, and hyperbolic systems of conservation laws. He includes explanatory materials on Huygen's principle for the wave equation on odd-dimensional spheres, hyperbolic polynomials references, the multiplicity of eigenvalues, mixed initial and boundary value problems, and in a contribution by Cathleen Morawetz, energy decay for star-shaped obstacles. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)