Electricity and magnetism are common features of our world. The subject of electromagnetic fields in empty space populated only by point charges or smooth charge distributions in space is well understood. In that case, one deals with the classical theory of electrodynamics developed by J.C. Maxwell in 1864. Electromagnetism in the presence of matter is, however, a completely different problem. Microscopic electric behavior of homogeneous substances can in general be characterized fairly simply and completely. The theory that enables us to do this is fairly well understood. Sadly the situation is quite different for magnetism in matter. The study there is phenomenological. That is, the substance is characterized by a number of parameters and the experimentally determined relations among them. We are not aware of any successful microscopic theory of magnetism in matter. The microscopic theory of magnetic substances, a topic of fundamental and technological importance, is the subject of this paper.