  The Bethe-Brueckner-Goldstone many-body theory of the Nuclear Equation of
State is reviewed in some details. In the theory, one performs an expansion in
terms of the Brueckner two-body scattering matrix and an ordering of the
corresponding many-body diagrams according to the number of their hole-lines.
Recent results are reported, both for symmetric and for pure neutron matter,
based on realistic two-nucleon interactions. It is shown that there is strong
evidence of convergence in the expansion. Once three-body forces are
introduced, the phenomenological saturation point is reproduced and the theory
is applied to the study of neutron star properties. One finds that in the
interior of neutron stars the onset of hyperons strongly softens the Nuclear
Equation of State. As a consequence, the maximum mass of neutron stars turns
out to be at the lower limit of the present phenomenological observation.
