  We present a pedagogical introduction to NRQED (non-relativistic quantum
electrodynamics). NRQED is an effective field theory that describes the
interaction of non-relativistic, possibly composite, spin-half particle with
the electromagnetic field. We explain in detail how the NRQED Lagrangian is
constructed up to and including order $1/M^2$, where $M$ is the mass of the
spin-half particle. As a sample application, we derive the Thomson scattering
cross section for the low energy scattering of a photon and a possibly
composite spin-half particle.
