For graduate mathematics students who have completed a rigorous course in partial differential equations, Rauch (mathematics, U. of Michigan)introduces hyperbolic versions of them. A major subtheme is linear and nonlinear geometric optics, along with the central results of linear microlocal analysis that are derived from them. Among the topics are simple examples of propagation, linear elliptical geometric optics, the nonlinear Cauchy problem, one-phase nonlinear geometric optics, resonant interaction and quasilinear systems, and dense oscillations for the compressible Euler equations. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)