  In this thesis we study the strongly-correlated-electron physics of the
longstanding H-Tc-superconductivity problem using a non-perturbative method,
the Dynamical Mean Field Theory (DMFT), capable to go beyond standard
perturbation-theory techniques. DMFT is by construction a local theory which
neglects spatial correlation. Experiments have however shown that the latter is
a fundamental property of cuprate materials. In a first step, we approach the
problem of spatial correlation in the normal state of cuprate materials using a
phenomenological Fermi-Liquid-Boltzmann model. We then introduce and develop in
detail an extension to DMFT, the Cellular Dynamical Mean Field Theory (CDMFT),
capable of considering short-ranged spatial correlation in a system, and we
implement it using the exact diagonalization algorithm . After benchmarking
CDMFT with the exact one-dimensional solution of the Hubbard Model, we employ
it to study the density-driven Mott metal-insulator transition in the
two-dimensional Hubbard Model, focusing in particular on the anomalous
properties of the doped normal state close to the Mott insulator. We finally
study the superconducting state. We show that within CDMFT the one-band Hubbard
Model supports a d-wave superconductive state, which strongly departs from the
standard BCS theory. We conjecture a link between the instabilities found in
the normal state and the onset of superconductivity.
