2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116395These notes are an introduction to basic properties of Andre-Quillen homology for commutative algebras. They are an expanded version of my lectures at the summer school: Interactions between homotopy theory and algebra, University of Chicago, 26th July - 6th August, 2004. The aim is to give fairly complete proofs of characterizations of smooth homomorphisms and of locally complete intersection homomorphisms in terms of vanishing of Andre-Quillen homology. The choice of the material, and the point of view, are guided by these goals.32 pages; to appear in: Interactions between homotopy theory and algebra (Chicago 2004), Contemp. MathCommutative AlgebraAlgebraic Topology13D03 (Primary); 18G30; 18G55 (Secondary)text