  General Relativity is the modern theory of gravitation. It has replaced the
newtonian theory in the description of the gravitational phenomena. In spite of
the remarkable success of the General Relativity Theory, the newtonian
gravitational theory is still largely employed, since General Relativity, in
most of the cases, just makes very small corrections to the newtonian
predictions. Moreover, the newtonian theory is much simpler, technically and
conceptually, when compared to the relativistic theory. In this text, we
discuss the possibility of extending the traditional newtonian theory in order
to incorporate typical relativistic effects, but keeping the simplicity of the
newtonian framework. We denominate these extensions neo-newtonian theories.
These theories are discussed mainly in the contexts of cosmology and compact
astrophysical objects.
