"Disorder is ubiquitous in nature and has a strong impact on the behaviour of many physical systems. The most celebrated effect of disorder is Anderson localization of single particles, but many other more complex phenomena arise in interacting, many-body systems. A full understanding of how disorder affects the behavior of quantum systems is still missing, also because of the unavoidable presence of nonlinearities, dissipation and thermal effects that make a careful exploration of real condensed-matter systems very difficult. In this project we want to fully exploit the unprecedented potentialities offered by ultracold atomic quantum gases to explore some of the present challenges for our understanding of the physics of disorder. These systems offer indeed the possibility of controlling to a great extent crucial parameters such as the type of disorder, the nonlinearities due to interactions, the temperature and density, the dimensionality, the quantum statistics. A variety of advanced diagnostic techniques allow to gain detailed information on the static and dynamic properties of the system. The potentialities of atomic quantum gases for the study of disorder have already showed up in recent breakthrough experiments. The project aims at an experimental exploration, supported by advanced theory, of the current issues in disordered quantum systems. We will investigate a few frontier themes of general interest: 1) Anderson localization and the interplay of disorder and a weak interaction; 2) strongly correlated, disordered bosonic systems; 3) disordered, interacting fermionic systems. In the research we will employ atomic Bose and Fermi gases with tunable interactions and advanced diagnostic techniques that we have recently contributed to develop. A successful completion of the project will push forward our understanding of the behaviour of quantum systems with disorder, with a potentially large impact on many fields of physics."