Chapters 10 and 11 consist of original research and are written in a more advanced style. In Chapter 10 it is shown that the structure of Maxwell's equations implies the existence of a wavelet analysis specifically adopted to electromagnetic radiation. The associated "eletromagnetic wavelets" are pulses parameterized by their point of origin and their scale, and can be made arbitrarily short by choosing fine scales. Furthermore, it is shown that every electromagnetic wave can be composed of such localized wavelets. This is applied in Chapter 11 to give a new formulation of radar based on electromagnetic wavelets. Since this theory is fully relativistic, its description of the Doppler effect is exact. In particular, it is three-dimensional, and does not make the usual assumption that the outgoing signal has a narrow bandwidth. Thus it should be useful in the construction of ultra-wideband radar systems.