2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33671We show that General Relativity (GR) with cosmological constant may be formulated as a rather simple constrained SO(D-1,2) (or SO(D,1))-Yang-Mills (YM) theory. Furthermore, the spin connections of the Cartan-Einstein formulation for GR appear as solutions of a genuine SO(D-1,1)-YM. We also present a theory of gravity with torsion as the most natural extension of this result. The theory comes out to be strictly an YM-theory upon relaxation of a suitable constraint. This work sets out to enforce the close connection between YM theories and GR by means of a new construction.8 pages. This replaced version has slightly modified title, some additional information that render our results clearer and a few new contributions. References addedGeneral Relativity and Quantum Cosmologytext