Cazenave (Pierre and Marie Curie University) reviews the fundamental properties of the linear Schrodinger equation and some results of local existence for the nonlinear Schrodinder equation in a general domain, then examines the local Cauchy problem, the regularity of solutions, the smoothing effect, global existence, finite-time blowup of solutions, the asymptotic behavior of solutions in the repulsive case, and the stability of standing waves in the attractive case. No index. Annotation (c) Book News, Inc., Portland, OR (booknews.com)