  We 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.
