The main objective in our research group is the use and development of quantum Monte Carlo simulation techniques, in order to study the behavior of ultracold quantum matter in the strongly and weakly interacting regimes. The proposal explained in this document constitues the natural extension of the scientific work carried out by our group along the years, thanks to the financial support received from the Ministerio for the last than fifty years. Once again and as done before, we join efforts with a research tem from the Universiad Pablo de Olavide in order to present a coordinated project. In summary, we plan to work on two main general topics: a) the analysis of ultracold microscopic quantum systems of bosons and fermions by means of Monte Carlo simulations, where their quantum nature is seen at a macroscopic level, and in different interaction regimes, dimensionalities, geometries, etc. b) the improvement of the simulation methods developed by our group (and others), as well as the dessign of new techniques in order to study new systems with different physics. In reference to point a), we plan to find: the phase diagram of dipolar fermions in 2D with arbitrary polarization strength and direction, the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature along the gas-stripe transition line for dipolar bosons and fermions, the emergence of several-particle bound states in few-body dipoles on a bilayer configuration, the phase diagram of bosons under synthetically created SOC interactions, the study and analysis of dipolar droplets and ultradilute liquid-like droplets in bosonic mixtures, as well as the analysis of polaron physics in one and two dimensions. We also plan to continue our study of Graphaite on Helium, and to study ultracold femi mixtures showing SU(N) symmetry. In reference to point b), we want to: analyze and build computer codes that implement time-dependent variational Monte Carlo techniques, allowing for the ground state optimization of bose and Fermi ground state wave functions, as well as provide accurate estimations of the (real time) dynamic structure function; extend our existing path integral ground state (PIGS) codes to evaluate the response function in complex time in many-body systems; and work in the design and implementation of diffusion Monte Carlo codes that include the sampling of systems with spin degrees of freedom in order to study Bose gases with SOC coupling.