Many of the aspects of relativistic quantum field theory have now been described, using the simple scalar theory to bring out the essential features. With the spin ½ theory also explained, we can turn at last to describe the theory of quantum electrodynamics and several of the experimental tests that verify it. Since to low order, the non-Abelian character of the strong interaction QCD theory plays no important role, there are QCD analogs of QED processes, and these will also be discussed. We begin by explaining the quantization of the electromagnetic field. This will be done in a way which is easily generalized to the non-Abelian case. We shall not discuss many of the traditional topics in QED which are well-described in several texts, but we will illustrate the character of the theory with an example of modern interest and with a traditional topic treated with modern methods. Thus we shall not discuss the traditional topics of relativistic Coulomb and Compton scattering, but we shall instead compute the cross section for e+ + e− → µ+ + µ− which is essentially the same as the quark-antiquark production in high-energy electron-positron collisions. The effects of vacuum polarization will be treated with modern methods, and it will be related to the e+e− cross section. The lowest order electron self energy and vertex functions will be calculated and their properties examined — one cannot avoid computing the magnetic moment of the electron.