  A quantum dissipation theory is formulated in terms of hierarchically coupled
equations of motion for an arbitrary electronic system coupled with grand
canonical Fermion bath ensembles. The theoretical construction starts with the
second--quantization influence functional in path integral formalism, in which
the Fermion creation and annihilation operators are represented by Grassmann
variables. Time--derivatives on influence functionals are then performed in a
hierarchical manner, on the basis of calculus--on--path--integral algorithm.
Both the multiple--frequency--dispersion and the non-Markovian reservoir
parametrization schemes are considered for the desired hierarchy construction.
The resulting formalism is in principle exact, applicable to interacting
systems, with arbitrary time-dependent external fields. It renders an exact
tool to evaluate various transient and stationary quantum transport properties
of many-electron systems. At the second--tier truncation level the present
theory recovers the real--time diagrammatic formalism developed by Sch\"{o}n
and coworkers. For a single-particle system, the hierarchical formalism
terminates at the second tier exactly, and the Landuer--B\"{u}ttiker's
transport current expression is readily recovered.
