  The paper provides a framework for a systematic analysis of the local BRST
cohomology in a large class of gauge theories. The approach is based on the
cohomology of s+d in the jet space of fields and antifields, s and d being the
BRST operator and exterior derivative respectively. It relates the BRST
cohomology to an underlying gauge covariant algebra and reduces its computation
to a compactly formulated problem involving only suitably defined generalized
connections and tensor fields. The latter are shown to provide the building
blocks of physically relevant quantities such as gauge invariant actions,
Noether currents and gauge anomalies, as well as of the equations of motion.
