**Financial support through the following projects:**

UID/MAT/00297/2019

UID/MAT/00297/2013

PEst-OE/MAT/UI0297/2014

PEst-OE/MAT/UI0297/2011

The topic of this presentation is the McKay Correspondence. This correspondence relates the finite subgroups of $SL(2,C)$, up to conjugation, with the Affine Simply laced Dynkin diagrams. With this result, a relation between distinct areas of mathematics is obtained. Finite Group Theory and Lie Algebras. This correspondence is also related with Algebraic Geometry. This means that we may obtain a better understanding of some results as we may consider those results in a more general context.

In order to show this correspondence, we could follow a different number of approaches: Representation Theory and Lie Algebras, Geometry, or Combinatorics. There are also some conceptual proofs.

We decided to follow an approach from Representation Theory, without using Lie Algebras, and from Combinatorics to present two different ways of proving the correspondence.