  We study three regimes of the Mott transitions characterized by classical,
marginally quantum and quantum. In the classical regime, the quantum degeneracy
temperature is lower than the critical temperature of the Mott transition, Tc,
below which the first-order transition occurs. The quantum regime describes the
Tc=0 boundary of the continuous transition. The marginal quantum region appears
sandwiched by these two regimes. The classical transition is described by the
Ising universality class. However, the Ginzburg-Landau-Wilson scheme breaks
down when the quantum effects dominate. The marginal quantum critical region is
categorized to a new universality class, where the order parameter exponent
beta, the susceptibility exponent gamma and the field exponent delta are given
by beta=d/2, gamma=2-d/2 and delta=4/d, respectively, with d being the spatial
dimensionality.The obtained universality classes agree with the recent
experimental results for organic conductors, kappa-(ET)2Cu[N(CN)2]Cl and
transition metal compounds such as V2O3. The mode coupling theory shows that
the marginal quantum criticality further generates non-Fermi-liquid properties
in the metallic side. A mechanism of high temperature superconductivity emerges
from the density fluctuations at small wavenumber. The mode coupling theory
combined with the Eliashberg equation predicts the superconductivity of the d
wave symmetry with the transition temperature of the correct order of magnitude
for the realistic parameters for the cuprate superconductors.
