2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123217We survey the analogy between Kleinian groups and subgroups of the mapping class group of a surface.27 pages. A survey to appear in the Proceedings of the 2005 Ahlfors--Bers ColloquiumGeometric TopologyGroup Theory20F65 (Primary); 30F60, 57M07, 57M50 (Secondary)text