This chapter discusses the propagation and diffraction of electromagnetic waves, and considers first the problem of determining the fields radiated by a known localised source in an unbounded medium. To determine the fields radiated by a known localised source in a linear homogeneous medium, we first take the temporal Laplace transform and spatial Fourier transform of Maxwell's equations. In this manner we obtain Laplace-Fourier representations of the fields, and angular-spectrum representations are subsequently obtained by applying contour integration to one of the Fourier integrals. This method was outlined in general terms by Felsen (1965,1970) and was used by Devaney (1971) to study radiation in a vacuum. The restriction imposed on the time behaviour of the basic quantities rules out the important case of time-harmonic sources and monochromatic fields. The same restriction guarantees, however, that each temporal Fourier component satisfies the Sommerfeld radiation condition.