  The modes of the electromagnetic field are solutions of Maxwell's equations
taking into account the material boundary conditions. The field modes of
classical optics - properly normalized - are also the mode functions of quantum
optics. Quantum physics adds that the excitation within each mode is quantized
in close analogy to the harmonic oscillator. A complete set of mode functions
forms a basis with which any new modes can be reconstructed. In full generality
each electromagnetic mode function in the four dimensional space-time is
mathematically equivalent to a harmonic oscillator. The quantization of the
electromagnetic field defines the excitation per mode and the correlation
between modes. In classical optics there can be oscillations and stochastic
fluctuations of amplitude, phase, polarization et cetera. In quantum optics
there are in addition uncertain quantum field components, quantum correlations
and quantized energies. Here, we present selected topics from classical to
quantum optics. We start in the second chapter with the classical optics
description of a light field and its spectral densities, their measurement and
their interpretation. In the third chapter the quantum properties of a single
light mode are reviewed as well as ways to measure these quantum properties.
Gaussian states of a light mode are emphasized, i. e. states for which the
Wigner function has a two dimensional Gaussian shape. The fourth chapter will
be concerned with more than one mode presenting a unifying approach to
quadratic Hamiltonians including phase conjugation which is related to time
reversal.
