  The canonical quantization of the essentially nonlinear midisuperspace model
describing cylindrically symmetric gravitational waves with two polarizations
is presented. A Fock space type representation is constructed. It is based on a
complete set of quantum observables. Physical expectation values may be
calculated in arbitrary excitations of the vacuum. Our approach provides a
non-linear generalization of the quantization of the collinearly polarized
Einstein-Rosen gravitational waves.
