From the Milnor number to the Le numbers

Certainly the most important numerical invariant of an isolated hypersurface singularity is its Milnor number. This number contains a crucial information about the singularity. For non-isolated singularities, the Milnor number (which is always infinite) is no longer relevant. However, for such singularities, D. Massey introduced a series of polar invariants which generalize the data given by the Milnor number for an isolated singularity. These polar invariants are called the Le numbers. In the first part of my talk, devoted to isolated singularities, I will review the basic theory of the Milnor number. In the second part, dedicated to non-isolated singularities, I will present Massey's theory of Le numbers.