  The use in the action integral of a volume element of the form $\Phi d^{D}x$
where $\Phi$ is a metric independent measure can give new interesting results
in all types of known generally coordinate invariant theories: (1) 4-D theories
of gravity plus matter fields; (2) Reparametrization invariant theories of
extended objects; (3) Higher dimensional theories. In the case (1), a large
number of new effects appears: under normal particle physics conditions
(primordial) fermions split into three families; when matter is highly diluted,
neutrinos increase their mass and can contribute both to dark energy and to
dark matter. In the case (2), it leads to dynamically induced tension; to
string models of non abelian confinement; to the possibility of new
Weyl-conformally invariant light-like branes which dynamically adjust
themselves to sit at black hole horizons; in the context of higher dimensional
theories it can provide examples of massless 4-D particles with nontrivial
Kaluza Klein quantum numbers. In the case (3), i.e. in brane and Kaluza Klein
scenarios, the use of a metric independent measure makes it possible to
construct naturally models where only the extra dimensions get curved and the
4-D remain flat.
