  This thesis focuses on modifications on Einstein's theory of General
Relativity, which could explain the current problems in gravitation and
cosmology. More specifically, modifications of the affine structure of the
spacetime, which is the structure that tells us how to perform derivatives, are
studied. These theories appear when imposing that the system must be invariant
under the action of the local Poincar\'e group. Within these theories, their
stability, the conditions for the appearance of singularities, the movement of
fermions, and if it is possible to find different Black Hole solutions than in
Einstein's theory, is explored. Moreover, a non-local extension of the
mentioned modification is proposed, which can make the theory free of
instabilities and singularities at the linear limit.
