  The theory of quantum propagator and time--dependent integrals of motion in
quantum optics is reviewed as well as the properties of Wigner function,
Q--function, and coherent state representation. Propagators and wave functions
of a free particle, harmonic oscillator, and the oscillator with varying
frequency are studied using time--dependent linear in position and momentum
integrals of motion. Such nonclassical states of light (of quantum systems) as
squeezed states, correlated states, even and odd coherent states (Schr\"odinger
cat states) are considered. Photon distribution functions of Schr\"odinger cat
male and female states are given, and the photon distribution function of
squeezed vacuum is derived using the theory of the oscillator with varying
parameters. Properties of multivariable Hermite polynomials used for the
description of the multimode squeezed and correlated light and polymode
Schr\"odinger cats are studied.
