F.B.I. Transformation : Second Microlocalization and Semilinear Caustics During the last ten years FBI transformation and second microlocalization have been used by several authors to solve different problems in the theory of linear or nonlinear partial differential equations. The aim of this book is to give an introduction to these topics in the spirit of the work ofSj|strand and to present their recent application to the propagation of conormal singularities for solutions of seminlinear hyperbolic equations due to Lebeau. The text is quite self contained and provides a useful entry to the subject and a bridging link to more specialized papers