2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131029We survey some recent results on the minimal graded free resolution of a square-free monomial ideal. The theme uniting these results is the point-of-view that the generators of a monomial ideal correspond to the maximal faces (the facets) of a simplicial complex Δ.26 pages; revised final version to appear in Contemporary Math; updated referencesCommutative AlgebraCombinatorics13D02, 13D40, 05C90, 05E99text