In Chap. 10 we obtained the full Maxwell Equations in the presence of charges and currents as sources. And in Chap. 1 Sect. 1.12.1 we encountered the experiments of Hertz, which identified the electromagnetic waves predicted by Maxwell. In this chapter we will solve Maxwell’s Equations in free space, without the presence of charges or currents as sources. This solution will provide us with a detailed picture of the structure of the electromagnetic waves that are possible in the context of classical electromagnetic field theory.