  K\"ahler-Chern-Simons theory describes antiself-dual gauge fields on a four-
dimensional K\"ahler manifold. The phase space is the space of gauge
potentials, the symplectic reduction of which by the constraints of
antiself-duality leads to the moduli space of antiself-dula instantons. We
outline the theory highlighting the symmetries, their canonical realization and
some properties of the quantum wave functions. The relationship to integrable
systems via dimensional reduction is briefly discussed.
