Phase space methods in quantum mechanics and optics

An account is given of the many ways in which methods based on phase space and the real symplectic groups can be fruitfully exploited in quantum mechanics and optics. These include the concept of generalised rays and action of optical systems on them; the properties of variance matrices for general n-dimensional quantum systems; a coset-space analysis of Gaussian pure states; a global approach to the concept of squeezing of multimode systems; and an intriguing instance of complementarity between Bose statistics for generalized rays and action of optical systems on them. (author). 19 refs