Introduction to microlocal analysis

The objective of this reading seminar is to provide an introduction to the theory of pseudodifferential operators. The main points of the lecture are: symbol spaces, pseudodifferential operators, composition theorems, symbolic calculus, Calderon-Vaillancourt theorem, inversion of elliptic operators, Garding theorem. The lecture will mainly follow chapter 1 of the book by S. Alinhac and P. Gérard (Pseudodifferential operators and Nash-Moser theorem).