This thesis is devoted to a study of the effect of disorder on strongly correlated electrons. For non-interacting electrons, Anderson localization occurs if the amount of disorder is sufficient. For disorder-free systems, a Mott metal-insulator transition may occur if the electron-electron interactions are strong enough. The question we ask in this thesis is what happens when both disorder and interactions are present. We study the Anderson-Hubbard model, which is the simplest model to include both interactions and disorder, using a Gutzwiller variational wave function approach. We then study Anderson localization of electrons from the response of the Anderson-Hubbard Hamiltonian to an external magnetic field. An Aharonov-Bohm flux induces a persistent current in mesoscopic rings. Strong interactions result in two competing tendencies: they tend to suppress the current because of strong correlations, and they also screen the disorder potential and making the system more homogenous. We find that, for strongly interacting electrons, the localization length may be large, even though the current is suppressed by strong correlations. This unexpected result highlights how strongly correlated materials can be quiet di erent from weakly correlated ones. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2011-08-31 09:51:47.155