See Alex Shannon’s essay.
Last chapter of Gelfand-Manin: Algebra V
http://ncatlab.org/nlab/show/D-module
http://ncatlab.org/nlab/show/D-geometry
arXiv:1206.1435 Three lectures on Algebraic Microlocal Analysis from arXiv Front: math.AG by Pierre Schapira 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.
nLab page on D-modules