An important application for electromagnetic radiation is the transmission of information. Monochromatic plane waves are not suited for this task because they contain practically no information other than their period ( \(\omega \) ). One can, however, modulate monochromatic plane waves and by this transfer information. Such a superposition of plane waves is most conveniently described in terms of Fourier series or Fourier integrals (in the continuum). In this chapter we will introduce such Fourier series, analyze their properties and find the general solution to the homogeneous wave equation.