  During the last 30 years, stimulated by the quest to build superconducting
quantum processors, a theory of quantum electrical circuits has emerged and
this theory goes under the name of circuit quantum electrodynamics or
circuit-QED. The goal of the theory is to provide a quantum description of the
most relevant degrees of freedom. The central objects to be derived and studied
are the Lagrangian and the Hamiltonian governing these degrees of freedom.
Central concepts in classical network theory such as impedance and scattering
matrices can be used to obtain the Hamiltonian and Lagrangian description for
the lossless (linear) part of the circuits. Methods of analysis, both classical
and quantum, can also be developed for nonreciprocal circuits. These lecture
notes aim at giving a pedagogical overview of this subject for
theoretically-oriented Master or PhD students in physics and electrical
engineering, as well as Master and PhD students who work on experimental
superconducting quantum devices and wish to learn more theory.
