In a volume based on courses he taught at Saint-Petersburg (Russia) and Rennes (France) Universities, Yafaev describes applications of scattering theory methods to differential operators, primarily the Schrödinger operator. In the first half of the volume, he presents a summary of and expands on the general scattering theory presented in Mathematical Scattering Theory: General Theory (AMS, 1992). Chapters illustrate basic theorems of abstract scattering theory, particularly their application to the perturbation of differential operators with constant coefficients and to the analysis of the trace class method. The second half is devoted to direct analytic methods applied to one-and multi-dimensional case problems (e.g., high- and low-energy asymptotics of the Green function, the scattering matrix, and ray and eikonal expansions). Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)