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In this thesis, I discuss the use of the Auxiliary Field Diffusion MonteCarlo method to compute the ground state of nuclear Hamiltonians, and I showseveral applications to interesting problems both in nuclear physics and innuclear astrophysics.  In particular, the AFDMC algorithm is applied to the study of several nuclearsystems, finite, and infinite matter. Results about the ground state of nuclei($^4$He, $^8$He, $^{16}$O and $^{40}$Ca), neutron drops (with 8 and 20neutrons) and neutron rich-nuclei (isotopes of oxygen and calcium) arediscussed, and the equation of state of nuclear and neutron matter arecalculated and compared with other many-body calculations. The $^1S_0$superfluid phase of neutron matter in the low-density regime was also studied.

The Auxiliary Field Diffusion Monte Carlo Method for Nuclear Physics and Nuclear Astrophysics