  Gauge theories that have been first quantized using the Hamiltonian BRST
operator formalism are described as classical Hamiltonian BRST systems with a
BRST charge of the form <\Psi,\Omega\Psi>_{even} and with natural ghost and
parity degrees for all fields. The associated proper solution of the classical
Batalin-Vilkovisky master equation is constructed from first principles. Both
of these formulations can be used as starting points for second quantization.
In the case of time reparametrization invariant systems, the relation to the
standard <\Psi,\Omega\Psi>_{odd} master action is established.
