  Theory of classical critical phenomena of Mott transition is developed for
the dimensionality $d \le \infty$. Reconsidering a cluster dynamical mean-field
theory (DMFT), Ginzburg-Landau free energy is derived in terms of hybridization
function for a cluster-impurity model. Its expansion around a cluster DMFT
solution reduces to a $\phi^4$ model. Inherent thermal Mott transition without
spontaneous symmetry breaking is described by a scalar field reflecting the
charge degrees of freedom. In the space of local Coulomb repulsion, chemical
potential and temperature, a first-order transition surface terminates at a
critical end curve. The criticality belongs to the Ising universality as a
liquid-gas transition. Various quantities including double occupancy, electron
filling and entropy show diverging responses at the criticality and
discontinuities at the first-order transition. Particularly, electron effective
mass shows a critical divergence in $2\le d\le 4$. Only at a certain curve on
the surface, a filling-control transition and its related singularities
disappear. We discuss detailed critical behaviors, effects of interplay with
other critical fluctuations, and relevant experimental results.
