On the 150th anniversary of Maxwell equations

In this lecture we discuss some interesting developments in the modern theory of electromagnetic field(s). In particular, by using the methods developed in Dirac's constraint dynamics we derive the Schr\"{o}dinger equation for the free electromagnetic field. The electromagnetic field that arises only contains combinations of transverse photons and does not include any scalar and/or longitudinal photons. This approach is also used to determine and investigate the actual symmetry of the free electromagnetic field. Then we discuss the Majorana representation of the Maxwell equations, the symmetric form of Maxwell equations and an original approach to electrodynamics called the "scalar electrodynamics".