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We study three regimes of the Mott transitions characterized by classical,marginally quantum and quantum. In the classical regime, the quantum degeneracytemperature is lower than the critical temperature of the Mott transition, Tc,below which the first-order transition occurs. The quantum regime describes theTc=0 boundary of the continuous transition. The marginal quantum region appearssandwiched by these two regimes. The classical transition is described by theIsing universality class. However, the Ginzburg-Landau-Wilson scheme breaksdown when the quantum effects dominate. The marginal quantum critical region iscategorized to a new universality class, where the order parameter exponentbeta, the susceptibility exponent gamma and the field exponent delta are givenby beta=d/2, gamma=2-d/2 and delta=4/d, respectively, with d being the spatialdimensionality.The obtained universality classes agree with the recentexperimental results for organic conductors, kappa-(ET)2Cu[N(CN)2]Cl andtransition metal compounds such as V2O3. The mode coupling theory shows thatthe marginal quantum criticality further generates non-Fermi-liquid propertiesin the metallic side. A mechanism of high temperature superconductivity emergesfrom the density fluctuations at small wavenumber. The mode coupling theorycombined with the Eliashberg equation predicts the superconductivity of the dwave symmetry with the transition temperature of the correct order of magnitudefor the realistic parameters for the cuprate superconductors.Comment: 47 pages including 8 figure

Universality classes of metal-insulator transitions in strongly correlated electron systems and mechanism of high-temperature superconductivity