Maxwell electrodynamics, complex rotation group, media

Our treatment will be with definite accents: the main attention is given to classical electrodynamics in material media, focusing on the structure of Minkowski constitutive relations, matrix complex form of Maxwell theory in the form of Riemann-Silberstein-Majorana-Oppenheimer, and the theory of complex rotation group, isomorphic to the Lorentz group. This review includes the topics: introduction; matrix complex form of Maxwell theory in a vacuum; modified Lorentz symmetry in electrodynamics; Minkowski electrodynamics in moving bodies; Minkowski constitutive relations in the complex 3-vector form; symmetry properties of the matrix equation in any linear media; Dirac matrices and electromagnetic field.