The generating functional technique and path integral representation were used to discuss the various properties of the closed time-path Green function and to work out a practical calculation scheme. It includes the ordinary quantum field theory and the classical fluctuation field theory as its limiting cases. It is well adapted to consider the symmetry breaking with either constituent or composite order parameters. The general formalism and the useful techniques are illustrated by applications to critical dynamics, quenched random systems, theory of nonlinear response, plasma, nuclear many-body problem and so on.--- won the honor of National Natural Science Award (second class), P.R.China in 2001.