The book consists of two parts. The first one is dedicated to the WKB methods and the semi-classical limit before the formation of caustics. The second part treats the semi-classical limit in the presence of caustics in the special geometric case where the caustic is reduced to a point (or to several isolated points). Both parts are essentially independent. The first part may be viewed simply as a motivation for the second part. Most of the content of the second part does not refer to WKB analysis. Also, the technical aspects are fairly independent in the two parts. The first part relies greatly on techniques coming from the study of hyperbolic partial differential equations,and especially, from quasi-linear ones. The second part is more typical of nonlinear Schr¨odinger equations in a way, since it involves scattering theory,
as well as Strichartz estimates related to Schr¨odinger equations.