  We present the derivation of the Yang-Mills gauge theory based on the
covariant Hamiltonian representation of Noether's theorem. As the starting
point, we re-formulate our previous presentation of the canonical Hamiltonian
derivation of Noether's theorem. The formalism is then applied to derive the
Yang-Mills gauge theory. The Noether currents of U(1) and SU(N) gauge theories
are derived from the respective infinitesimal generating functions of the
pertinent symmetry transformations which maintain the form of the Hamiltonian.
