During the last ten years, FBI transformation and secondmicrolocalization have been used by several authors to solvedifferent problems in the theory of linear or nonlinearpartial differential equations. The aim of this book is togive an introduction to these topics, in the spirit of thework ofSj-strand, and to present their recent applicationto the propagation of conormal singularities for solutionsof seminlinear hyperbolic equations, due to Lebeau. The textis quite self-contained and provides a useful entry to thesubject and a bridging link to more specialized papers.