Symmetries are everywhere: we can find them in nature, art, music, poetry... we can find them in equations, geometrical objects, mechanical systems, molecules and more generally, all over mathematics and science. But what are they? Why are they so important? Every mathematician, even without noticing it, has used symmetries to solve problems which otherwise would have been more difficult or even impossible to solve. 

The talk will be a journey into group theory: the branch of mathematics which studies the concept of symmetries and how they relate to one another. We will focus in particular on finite groups and how they are built by fundamental blocks: the finite simple groups, whose classification is considered one of the most remarkable achievements in the mathematics of the last century. We will talk about how some of today's research problems, such as generation problems, can be encoded in the language of graphs which help us to better understand the structure of finite groups.