  In this Thesis, we report a detailed study of the ground-state properties of
a set of quantum few- and many-body systems in one and two dimensions with
different types of interactions by using Quantum Monte Carlo methods.
Nevertheless, the main focus of this work is the study of the ground-state
properties of an ultracold Bose system with dipole-dipole interaction between
the particles. We consider the cases where the bosons are confined to a bilayer
and multilayer geometries, that consist of equally spaced two-dimensional
layers. These layers can be experimentally realized by imposing tight
confinement in one direction. We specifically address the study of new quantum
phases, their properties, and transitions between them. One expects these
systems to have a rich collection of few- and many-body phases because the
dipole-dipole interaction is anisotropic and quasi long-range.
