A CIMPA school on Serre's big image theorem for Galois representation associated to elliptic curves Universidad de Valparaiso, Valparaiso, Chile January 617, 2025 

The purpose of the school is to present a selfcontained proof of a famous theorem of Serre in 1972. This theorem tells us that the representation associated to the Galois action on the ptorsion points of an elliptic curve is surjective for p great enough. This theorem had a very great impact in the field of arithmetic geometry and opened the field to numerous problems that are, for some, still open today. After introducing the students to the topics needed to understand the proof, illustrating the theory through exercises and computer sessions , we will present the proof itself.
