An Introduction to D-Modules

The theory of D-modules had initially been developed for complex (algebraic and analytic) varieties in the 1970's, and allows for an algebraic approach of partial differential equations. There are lots of applications; for instance, in the 1980's Masaki Kashiwara and Zoghman Mebkhout have used it to generalize the Riemann-Hilbert correspondence. D-modules are also an invaluable tool in less expected areas, such as Representation Theory. In more recent years, D-modules have also found applications to the world of arithmetic varieties.