2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113898These notes are based on a course for a general audience given at the Centro de Modeliamento Matemático of the University of Chile, in December 2004. We study the mean convergence of multiple ergodic averages, that is, averages of a product of functions taken at different times. We also describe the relations between this area of ergodic theory and some classical and some recent results in additive number theory.Dynamical Systems37A05text