The formal theory of waves is developed by solving the wave equation. The condition for a solution to exist leads to a dispersion equation, and each specific solution of this equation is called the dispersion relation for a particular wave mode. An arbitrary wave mode is referred to as “the mode M”. The polarization vector for the mode M is defined as a unimodular vector along the direction of the electric vector found by solving the wave equation for waves in the mode M. Specific examples of wave modes are discussed for isotropic media, anisotropic crystals and cold magnetized plasmas. Transverse waves in a isotropic medium correspond to two degenerate wave modes, and the description of their polarization is discussed separately.