  In this thesis, the ground state properties of nuclear matter, namely the
energy per particle and the response to weak probes, are computed, studying the
effects of three nucleon interactions. Both the variational approach, based on
the formalism of correlated basis function, and the auxiliary field diffusion
Monte Carlo method have been used. A scheme suitable to construct a
density-dependent two-nucleon potential in correlated basis approach is
discussed. The density dependent potential resulting from UIX three-nucleon
force has been employed in auxiliary field diffusion Monte Carlo calculations
that turned out to be in very good agreement with correlated basis variational
results. Hence, the underbinding of symmetric nuclear matter has to be ascribed
to deficiencies of the UXI potential. A comparative analysis of the equations
of state of both pure neutron matter and symmetric nuclear matter obtained
using a new generation of "chiral inspired" local three-body potentials has
been performed. These potentials provide an excellent description of the
properties of light nuclei, as well as of the neutron-deuteron doublet
scattering length. The weak response of symmetric nuclear matter has been
computed at three-body cluster level. Two-body effective interactions and
one-body effective operators have been derived within the formalism of
correlated basis functions. The inclusion of the three-body cluster term in the
effective interaction allowed for a direct inclusion of the UIX three-nucleon
potential. Moreover, the sizable unphysical dependence of the effective weak
operator is removed once the three-body cluster term is taken into account.
