The main topic of the book is higher analytic microlocalization and its application to problems ofpropagation of singularities. The part on highermicrolocalization could serve as an introduction to thesubject. The results on propagation refer to solutions oflinear partial differentialoperators with characteristicsof variable multiplicity and are of conical refraction type.The relation and interplay between these results and resultsor constructions from geometrical optics in crystal theoryis discussed with many details. The notes are writtenforemost for researchers working in microlocal analysis,but it is hoped that they can also be of interest formathematicians and physicists who work in propagationphenomena from a more classical point of view.