  This talk is assumed to exhibit an overview of the quantum theory for
mesoscopic electric circuits and some of its further developments. In the
theory the importance of the discreteness of electronic charge in mesoscopic
electric circuit is addressed. The mesoscopic LC-design is quantized in accord
with the charge discreteness. The uncertainty relation for electric charge and
current is given. Because the stationary Schr\"odinger equation is turned to be
Mathieu equation in $p$-representation, the wave function and energy spectrum
is formally solved. As further applications, the persistent current is obtained
by considering the mesoscopic ring as a pure L-design. The Coulomb blockade
phenomenon occurs when applying the theory to the pure C-design. Concerning the
time evolution of the states for mesoscopic electric circuit, we are able to
study it by the method of characteristics. In order to study the dissipative
effect in the circuit, we use density-matrix formulation. In this formulation,
several type of ``off diagonal'' dissipations are expected to be discussed.

Mesoscale and Nanoscale Physics