We introduce the vacuum Maxwell equations and use them to describe electromagnetic fields trapped in a cavity. Boundary conditions for the cavity are shown to lead to standing wave solutions which we quantize to construct cavity QED, a quantum theory for those fields. We insert a rotor into the cavity and are led to a quantum description of a rotor(atom) qubit coupled to a quantized electromagnetic field. We derive the Jaynes-Cummings Hamiltonian and find its approximate eigenvalues and eigenvectors in the strong atom-radiation coupling regime. We show how artificial atoms, composed of superconducting Josephson junctions, interact with microwave line-resonator photons, thus allowing a circuit analog of cavity QED. We discuss how the latter is described with electrical circuit terminology.