Microlocal analysis is a geometric theory of distributions, describing techniques developed during the past centuary based on Fourier transforms related to the study of inear and nonlinear partial differential equations. This includes generalized functions, pseudo-differential operators and Fourier integral operators. The term microlocal implies localisation not just at a point, but in terms of cotangent space directions at a given point.

The main topics of the course are:
1. Theory of distributions.
2. Method of stationary phase
3. Pseudo-differential operators.
4. Application to elliptic operators
5. The zeta function of an elliptic operator.
6. Asymptotic behavior of the spectral counting function.