  Both magnetic materials and light have always played a predominant role in
information technologies, and continue to do so as we move into the realm of
quantum technologies. In this course we review the basics of magnetism and
quantum mechanics, before going into more advanced subjects. Magnetism is
intrinsically quantum mechanical in nature, and magnetic ordering can only be
explained by use of quantum theory. We will go over the interactions and the
resulting Hamiltonian that governs magnetic phenomena, and discuss its
elementary excitations, denominated magnons. After that we will study
magneto-optical effects and derive the classical Faraday effect. We will then
move on to the quantization of the electric field and the basics of optical
cavities. This will allow us to understand a topic of current research
denominated Cavity Optomagnonics. These notes were written as the accompanying
material to the course I taught in the Summer Semester 2018 at the
Friedrich-Alexander University in Erlangen. The course is intended for Master
or advanced Bachelor students. Basic knowledge of quantum mechanics,
electromagnetism, and solid state at the Bachelor level is assumed. Each
section is followed by a couple of simple exercises which should serve as to
"fill in the blanks" of what has been derived, plus specific references to
bibliography, and a couple of check-points for the main concepts developed. The
figures are pictures of the blackboard taken during the lecture.
