  We present a detailed derivation of a microscopic theory for the glass
transition of a liquid enclosed between two parallel walls relying on a
mode-coupling approximation. This geometry lacks translational invariance
perpendicular to the walls, which implies that the density profile and the
density-density correlation function depends explicitly on the distances to the
walls. We discuss the residual symmetry properties in slab geometry and
introduce a symmetry adapted complete set of two-point correlation functions.
Since the currents naturally split into components parallel and perpendicular
to the walls the mathematical structure of the theory differs from the
established mode-coupling equations in bulk. We prove that the equations for
the nonergodicity parameters still display a covariance property similar to
bulk liquids.
