  We introduce a symplectic structure on the space of connections in a
G-principal bundle over a four-manifold and the Hamiltonian action on it of the
group of gauge transformations which are trivial on the boundary. The
symplectic reduction becomes the moduli space of flat connections over the
manifold. On the moduli space of flat connections we shall construct a
hermitian line bundle with connection whose curvature is given by the
symplectic form. This is the Chern-Simons prequantum line bundle. The group of
gauge transformations on the boundary of the base manifold acts on the moduli
space of flat connections by an infinitesimally symplectic way. This action is
lifted to the prequantum line bundle by its abelian extension.
