In order to relate the electromagnetic field to its sources one needs to solve Maxwell's equations. One method of solving Maxwell's equations is to introduce potentials (the scalar and vector potentials) which effectively reduces the number of independent equations. For static sources and fields one may reduce Maxwell's equations to Poisson's equation for the electromagnetic potentials, and for time-dependent sources and fields one may reduce Maxwell's equations to d'Alembert's equation for the electromagnetic potentials. An alternative approach is to Fourier transform. This approach applies only to fluctuating fields, and hence it is necessary to distinguish between fluctuating fields and any static field, which is regarded as an ambient field when describing the response to fluctuating fields using Fourier transforms. The use of Fourier transforms allows one to reduce Maxwell's equations for time-dependent sources and fields to a single algebraic equation, called the wave equation. A specific advantage of this approach is that it allows one to include the effect of an ambient medium in a simple but general way.

Maxwell's equations are written down and the electromagnetic potentials are introduced in Chapter 1. There are two mathematical tools that are required in the treatment of electromagnetic theory adopted here. One of these is tensor algebra, which is introduced in Chapter 2. Some electromagnetic applications of tensor algebra are described in Chapter 3 with particular emphasis on multipole moments. The other mathematical tool is the Fourier transformation, which is introduced in Chapter 4.