  The issue of the transformations of units is treated, mainly, in a
geometrical context. It is shown that Weyl-integrable geometry is a consistent
framework for the formulation of the gravitational laws since the basic law on
which this geometry rests is invariant under point-dependent transformations of
units. Riemann geometry does not fulfill this requirement. Spacetime
singularities are then shown to be a consequence of a wrong choice of the
geometrical formulation of the laws of gravitation. This result is discussed,
in particular, for the Schwrazschild black hole and for
Friedmann-Robertson-Walker cosmology. Arguments are given that point at
Weyl-integrable geometry as a geometry implicitly containing the quantum
effects of matter. The notion of geometrical relativity is presented. This
notion may represent a natural extension of general relativity to include
invariance under the group of units transformations.
