Geomtrically, it is a correspondence between the group theory (representation or conjugacy class) and the topology of a resolution of the singularity. Recently we have many generalization of this correspondece, not only in Mathematics but also in Physics.

I will talk on a brief history of the McKay correspondence and introduce a way to calculate the cohomological invariants using group theoretical objects. In this process, we will meet various topics, i.e., algebraic geometry, representation theory, combinatorics, and so on. However, I will try to talk on the correspondence without assuming any special knowledge of them.