  The symmetry studies of Maxwell equations gave new insight on the nature of
electromagnetic (EM) field. Tey are reviewed in the work presented. It is
drawing the attention on the following aspects.
  EM-field has in general case quaternion structure, consisting of four
independent field constituents, which differ from each other by the parities
under space inversion and time reversal.
  There exists physical conserving quantity, which is simultaneously invariant
under both Rainich dual and additional hyperbolic dual symmetry transformation
of Maxwell equations. It is spin in general case or spirality in the
corresponding geometry.
  Generalized Maxwell equations for quaternion four-component EM-field are
obtained.
  Invariants for EM-field, consisting of dually symmetric parts are found.
  The main postulate of quantum mechanics: "To any mechanical quantity can be
set up in the correspondence the Hermitian matrix by quantization" was proved.
  Canonical Dirac quantization method was developed in two aspects. The first
aspect is its application the only to observable quantities. The second aspect
is the realization along with well known time-local quantization of space-local
quantization and space-time-local quantization. It is also shown, that Coulomb
field can be quantized in 1D and 2D systems.
  The photons in quantized EM-field are main excitations in oscillator
structure of EM-field, which is equivalent to spin S = 1 "boson-atomic" 1D
lattice structure, consisting of the "atoms" with zeroth rest mass. The photons
of the first kind and of the second kind represent themselves respectively
neutral chargeless spin 1/2 EM-solitons and charged spinless EM-solitons of
Su-Schrieffer-Heeger family.
