2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107449Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by Drinfeld, Dugger-Shipley, ..., Toen and Toen-Vaquie.30 pages, correction at the end of 3.9, corrections and added references in 5.7K-Theory and HomologyAlgebraic Geometry18E30; 16D90text