2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/34310This paper surveys aspects of the convergence and degeneration of Riemannian metrics on a given manifold M - the Cheeger-Gromov theory - and extensions thereof to Ricci curvature in place of full curvature. This theory is then applied to study a collection of different issues in mathematical aapects of General Relativity.23pp, for Proc. 2002 Cargese School on General RelativityGeneral Relativity and Quantum CosmologyDifferential Geometrytext