  After giving an outline of the quantization scheme based on the microscopic
Hopfield model of a dielectric bulk material, we show how the classical
phenomenological Maxwell equations of the electromagnetic field in the presence
of dielectric matter of given space- and frequency-dependent complex
permittivity can be transferred to quantum theory. Including in the theory the
interaction of the medium-assisted field with atomic systems, we present both
the minimal-coupling Hamiltonian and the multipolar-coupling Hamiltonian in the
Coulomb gauge. To illustrate the concept, we discuss the input--output
relations of radiation and the transformation of radiation-field quantum states
at absorbing four-port devices, and the spontaneous decay of an excited atom
near the surface of an absorbing body and in a spherical micro-cavity with
intrinsic material losses. Finally, we give an extension of the quantization
scheme to other media such as amplifying media, magnetic media, and nonlinear
media.
