Higher order wave front sets -- Pseudodifferential operators -- Bi-symplectic geometry and multihomogeneous maps -- Fourier Integral Operators -- Conical refraction, hyperbolicity and slowness surfaces -- Propagation of regularity up to the boundary -- Some results on transmission problems -- Partial analyticity, higher microlocalization and sheaves.

The main topic of the book is higher analytic microlocalization and its application to problems of propagation of singularities. The part on higher microlocalization could serve as an introduction to the subject. The results on propagation refer to solutions of linear partial differentialoperators with characteristics of variable multiplicity and are of conical refraction type. The relation and interplay between these results and results or constructions from geometrical optics in crystal theory is discussed with many details. The notes are written foremost for researchers working in microlocal analysis, but it is hoped that they can also be of interest for mathematicians and physicists who work in propagation phenomena from a more classical point of view.