  Electromagnetism in substance is characterized by permittivity (dielectric
constant) and permeability (magnetic permeability). They describe the substance
property {\it effectively}. We present a {\it geometric} approach to it. Some
models are presented, where the two quantities are geometrically defined.
Fluctuation due to the micro dynamics (such as dipole-dipole interaction) is
taken into account by the (generalized) path-integral. Free energy formula
(Lifshitz 1954), for the material composed of three regions with different
permittivities, is explained. Casimir energy is obtained by a new
regularization using the path-integral. Attractive force or repulsive one is
determined by the sign of the {\it renormalization-group} $\beta$-function.
