  This work is focused on the theory of Gravitoelectromagnetism (GEM). In the
first part of this work we present a brief review of gravitoelectromagnetism,
we locate and discuss all the problems which appear in this approach. We also
try to avoid these problems by proposing new approaches in which we use the
additional degrees of freedom of the gravitational field. In the second part of
this work, we review our previous work regarding the construction of a
tensorial theory, using the formalism of General Relativity, which aims to
describe the true electromagnetism. We also extend this theory in order to make
it more realistic. Finally in the third part of this work, we investigate the
existence of gravitational invariants similar to the electromagnetic ones.
