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A novel approach to Quantum Mechanics, the Conformal Quantum Geometrodynamics (CQG), is presented based on Weyl's differential geometry and Weyl's conformal gauge invariance. Following Weyl's statement that "it is in the nature of metrical space to be furnished with a non trivial affine relationship" (i.e. a non trivial law for the vector parallel transport) we assume that even if the metric of the space is Eulclidean or Minkowski, the space is nonetheless curved. We show moreover that this unavoidable curvature of space originates quantum effects. The CQG provides a deterministic, local and complete model of the standard Quantum Mechanics founded on the general requirement of Weyl's gauge invariance, i.e. invariance under arbitrary local scale change (calibration). The usual statistical and nonlocal interpretation of Quantum Mechanics is obtained in only in a particular Weyl gauge (reckoned the "natural" gauge), but in general the only possible interpretation of the theory is geometrical. Being a deterministic and complete theory, when applied to spin 1/2 pair the CQG solves the EPR (and other) paradoxes and allows a simple geometrical explanation of Pauli's exclusion principle in both the relativistic and nonrelativistic case. Finally, last but not least, the CQG provides a common language to Quantum Mechanics and General Relativity.