2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135827These lecture notes provide a pedagogical introduction to a specific continuum implementation of the Wilsonian renormalization group, the effective average action. Its general properties and, in particular, its functional renormalization group equation are explained in a simple scalar setting. The approach is then applied to Quantum Einstein Gravity (QEG). The possibility of constructing a fundamental theory of quantum gravity in the framework of Asymptotic Safety is discussed and the supporting evidence is summarized.Based on lectures given by M.R. at the ``First Quantum Geometry and Quantum Gravity School'', Zakopane, Poland, March 2007, and the ``Summer School on Geometric and Topological Methods for Quantum Field Theory'', Villa de Leyva, Colombia, July 2007, and by F.S. at NIKHEF, Amsterdam, The Netherlands, June 2006High Energy Physics - Theorytext