2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153598We recall the definition of $q$-differential algebras and discuss some representative examples. In particular we construct the $q$-analog of the Hochschild coboundary. We then construct the universal $q$-differential envelope of a unital associative algebra and study its properties. The paper also contains general results on $d^N=0$.24 pages, Latex2e, uses pb-diagram, available at http://qcd.th.u-psud.frQuantum Algebratext