Electrodynamics is the branch of physics which deals with rapidly changing electric and magnetic fields. "Rapidly changing", in this context, means that simple mid-19th century descriptions of changing fields, such as Faraday's law and the Biot-Savart law are inaccurate. In practice, this means the study of electromagnetic radiation or light.
Electrodynamics is the most advanced form of classical electromagnetism. Many results in electrodynamics are an attempt to explain previously known optical laws, such as Snell's law, by using appropriately simplified versions of Maxwell's equations; and to explain phenomena such as scattering and absorbance of light.
Albert Einstein developed special relativity through an examination of electrodynamics. During the late 19th century, physicists noted a contradiction between the accepted laws of electrodynamics and those of classical mechanics. In particular, Maxwell's equations predicted counterintuitive results such as that the speed of light was the same to all observers and did not obey Galilean invariance. It was believed therefore that Maxwell's equations were incorrect and that the actual equations of electromagnetism contained a term which corresponded to the influence of the "luminiferous aether".
After experiments failed to find evidence of the aether, Einstein proposed the revolutionary idea that the equations of classical electrodynamics were correct and that the equations of classical mechanics were incorrect. This led to the development of special relativity.
Quantum electrodynamics, as the name suggests, is the quantum mechanical theory of electrodynamics. It centres around a description of the photon – the particle of light which does not exist in classical electrodynamics.
See also: electromagnetism