  Several dynamical symmetries of the Dirac Hamiltonian are reviewed in a
systematic manner and the conditions under which such symmetries hold. These
include relativistic spin and orbital angular momentum symmetries, SO(4)\times
SU_{\sigma}(2) symmetry for the Dirac Hydrogen atom, SU(3)\times SU_{\sigma}(2)
symmetry for the relativistic simple harmonic oscillator. The energy spectrum
in each case is calculated from group-theoretic considerations.
