An introduction to V-filtrations

We give an introduction to the theory of V-filtrations of Malgrange and Kashiwara. After discussing the basic properties of this construction (in the case of a smooth hypersurface and, later, in the general case), we describe the connection with the theory of b-functions. As an example, we treat the case of weighted homogeneous isolated singularities. We discuss the compatibility of V-filtrations with proper push-forward and duality and the connection with nearby and vanishing cycles via the Riemann-Hilbert correspondence. We end by describing some invariants of singularities via the V-filtration.