There will be five lectures on characteristic classes. The first two lectures will be delivered by Laurentiu Maxim, while Joerg Schuermann will give the last three lectures. The plan for our lectures is as follows:

Lecture 1 (by L. Maxim): (Multiplicative) Characteristic classes of vector bundles, examples (Chern and L-class), characteristic classes of smooth manifolds, the signature and Poincare-Hopf theorems.

Lecture 2 (by L. Maxim): L-classes via the Pontrjagin construction, first for smooth, then for stratified rational homology manifolds (hinting to the Goresky-MacPherson classes defined via intersection homology)

Lecture 3 (by J. Schuermann): Calculus of constructible functions for Whitney stratified spaces

Lecture 4 (by J. Schuermann): Stratified Morse theory for constructible functions and lagrangian cycles, Poincare-Hopf for singular spaces

Lecture 5 (by J. Schuermann): Chern classes of complex singular spaces via lagrangian cycles.