  Albert Einstein's General Relativity (GR) from 1916 has become the widely
accepted theory of gravity and been tested observationally to a very high
precision at different scales of energy and distance. At the same time, there
still remain important questions to resolve. At the classical level
cosmological and black hole singularities are examples of problems which let us
notice that GR is incomplete at short distances (high energy). Furthermore, at
the quantum level GR is not ultraviolet (UV) complete, namely it is not
perturbatively renormalizable. Most of the work try to solve these problems
modifying GR by considering finite higher order derivative terms. Fourth
Derivative Gravity, for example, turns out to be renormalizable, but at the
same time it introduces ghost. To avoid both UV divergence and presence of
ghost one could consider sets of infinite higher derivative terms that can be
expressed in the form of entire functions satisfying the special property do
not introduce new poles other than GR graviton one. By making a special choice
for these entire functions, one could show that such a theory describes a
gravity that, at least in the linear regime, can avoid both the presence of
ghost and classical singularities (both black hole and cosmological
singularities). In this master's thesis we review some of these aspects
regarding gravitational interaction, focusing more on the classical level. Most
of the calculations are done in detail and an extended treatment of the
formalism of the spin projector operators is presented.
