2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122243This paper overviews recent developments in the classification up to quasi-isometry of finitely generated groups, and more specifically of relatively hyperbolic groups.These notes are based on a series of lectures given at the summer school ``Géométries à courbure négative ou nulle, groupes discrets et rigidités'' held in GrenobleGeometric TopologyGroup Theorytext