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.