Introduction to D-Modules

D-modules are modules over the ring of linear differential operators. They can be thought of as the geometric approach to systems of complex linear PDE. Introducing D-modules to the geometric representation theory led to proofs of various long-standing conjectures. The language of D-modules is used in the formulation of the geometric Langlands correspondence.

I will give a gentle introduction to D-modules. I will try to keep the prerequisites to the minimum.