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In this thesis we study the strongly-correlated-electron physics of thelongstanding H-Tc-superconductivity problem using a non-perturbative method,the Dynamical Mean Field Theory (DMFT), capable to go beyond standardperturbation-theory techniques. DMFT is by construction a local theory whichneglects spatial correlation. Experiments have however shown that the latter isa fundamental property of cuprate materials. In a first step, we approach theproblem of spatial correlation in the normal state of cuprate materials using aphenomenological Fermi-Liquid-Boltzmann model. We then introduce and develop indetail an extension to DMFT, the Cellular Dynamical Mean Field Theory (CDMFT),capable of considering short-ranged spatial correlation in a system, and weimplement it using the exact diagonalization algorithm . After benchmarkingCDMFT with the exact one-dimensional solution of the Hubbard Model, we employit to study the density-driven Mott metal-insulator transition in thetwo-dimensional Hubbard Model, focusing in particular on the anomalousproperties of the doped normal state close to the Mott insulator. We finallystudy the superconducting state. We show that within CDMFT the one-band HubbardModel supports a d-wave superconductive state, which strongly departs from thestandard BCS theory. We conjecture a link between the instabilities found inthe normal state and the onset of superconductivity.

Investigation of Strongly Correlated Electron Systems with Cellular Dynamical Mean Field Theory