Two-dimensional fermionic systems show remarkable physical properties, not only of interest for fundamental science but also directed towards technological application. Two paradigmatic examples are layered high-Tc superconductors and graphene. However, despite of decades of investigations, their theoretical comprehension is far from being complete.In QuFerm2D, I propose to use atomic Fermi gases to study the physics of two-dimensional strongly correlated fermions. Indeed, ultracold atoms are “ideal” quantum simulators of many-body phenomena thanks to the unprecedented possibility of controlling most of the relevant parameters. I want to set up a new machine that will benefit of the recent advances in ultracold atomic system, such as single-site addressability and the full control of the interparticle interactions. Tailoring arbitrary optical potentials will create the perfect environment for implementing quantum models.I want to characterize both the normal and the superfluid phases of layered fermions. At high temperatures I will measure the equation of state to check the validity of the Fermi liquid description, pointing out also the role of fluctuations. In the superfluid regime, I will study the interlayer tunneling, discriminating the coherent Josephson dynamics from the single-particle hopping, and determining the superfluid energy gap. By adding disorder I want to simulate the physics of granular superconductors, testing the robustness of the order parameter and the onset of metallic phases at higher temperatures. The comprehension of these topics will be the natural background to implement the many-body Fermi-Hubbard Hamiltonians in square and honeycomb lattices that are expected to unveil the microscopic mechanisms of high-Tc superconductors and of graphene in presence of strong interactions.I believe that the successful realization of this project will shed new light on the exciting and interdisciplinary field of strongly correlated fermions.