These three lectures present some fundamental and classical aspects of
microlocal analysis. Starting with the Sato's microlocalization functor and the
microsupport of sheaves, we then construct a microlocal analogue of the
Hochschild homology for sheaves and apply it to recover index theorems for
D-modules and elliptic pairs. In the third lecture, we construct the
ind-sheaves of temperate and Whitney holomorphic functions and give some
applications to the study of irregular holonomic D-modules.Comment: small correction
