2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161574We give a self-contained presentation of the basic results on jet schemes of singular varieties. Applications are given to invariants of singularities, such as minimal log discrepancies. We simplify our older approach to Inversion of adjunction for locally complete intersection varieties, and we prove a more general result for arbitrary Q-Gorenstein varieties embeded in nonsingular varieties (this statement has been proved independently also by Kawakita) .42 pages; v2: revised version, to appear in the proceedings of the 2005 AMS Summer Research Institute in Algebraic GeometryAlgebraic Geometry14B05, 14E30text