  Dirac's quantization of the Maxwell theory on non-commutative spaces has been
considered. First class constraints were found which are the same as in
classical electrodynamics. The gauge covariant quantization of the non-linear
equations of electromagnetic fields on non-commutative spaces were studied. We
have found the extended Hamiltonian which leads to equations of motion in the
most general gauge covariant form. As a special case, the gauge fixing approach
on the basis of Dirac's brackets has been investigated. The problem of the
construction of the wave function and physical observables have been discussed.
