In this chapter we consider gauge fields. The simplest example of a gauge field is the electromagnetic field. A straightforward generalization of the boson quantization considered above is not possible for these fields, because, like fermion systems, gauge theories are singular. A theory is called singular if there are velocities which cannot be expressed in terms of coordinates and momenta and so the standard Hamiltonian representation is not plausible. The quantization of such fields require a more serious modification than was necessary for the case of fermions. Let us start by recalling some facts about classical gauge theory.