Since a very long time ago, there has been an effective approach to study geometry via group theory. In this talk, we will focus on objects given by sets of solutions of a system of polynomial equations, called algebraic varieties. Galois theory makes a bridge between the geometry of algebraic varieties and group theory in terms of Galois representations. 

The talk will survey some basic but still interesting aspects of these connections and provide several examples. We will also provide a uniform way to investigate a certain class of algebraic varieties, named Abelian varieties.