InElectrodynamics the previous chapters we have described the general framework for the description of gauge theories in terms of noncommutative manifolds. The present chapter serves two purposes. First, we describe abelian gauge theories within the framework of noncommutative geometry, which at first sight appears to be a contradictio in terminis. Second, in Sect. 11.2 we show how this example can be modified to provide a description of one of the simplest examples of a field theory in physics, namely electrodynamicsElectrodynamics. Because of its simplicity, it helps in gaining an understanding of the formulation of gauge theories in terms of almost-commutative manifoldsAlmost-commutative manifold, and as such it provides a first stepping stone towards the derivationDerivation of the Standard Model from noncommutative geometry in Chap. 13 .