  In this paper we show how a gravitational field generated by a given
energy-momentum distribution (for all realistic cases) can be represented by
distinct geometrical structures (Lorentzian, teleparallel and non null
nonmetricity spacetimes) or that we even can dispense all those geometrical
structures and simply represent the gravitational field as a field, in the
Faraday's sense, living in Minkowski spacetime. The explicit Lagrangian density
for this theory is given and the field equations (which are a set of four
Maxwell's like equations) are shown to be equivalent to Einstein's equations.
We also analyze if the teleparallel formulation can give a mathematical meaning
to "Einstein's most happy thought", i.e. the equivalence principle. Moreover we
discuss the Hamiltonian formalism for for our theory and its relation to one of
the possibles concepts for energy of the gravitational field which emerges from
it and the concept of ADM energy. One of the main results of the paper is the
identification in our theory of a legitimate energy-mometum tensor for the
gravitational field expressible through a really nice formula.
