  This is a survey of `Cohomological Physics', a phrase that first appeared in
the context of anomalies in gauge theory. Differential forms were implicit in
physics at least as far back as Gauss (1833) (cf. his electro-magnetic
definition of the linking number), and more visibly in Dirac's magnetic
monopole (1931). The magnetic charge was given by the first Chern number. Thus
were characteristic classes (and by implication the cohomology of Lie algebras
and of Lie groups) introduced into physics. The `ghosts' introduced by Fade'ev
and Popov were incorporated into what came to be known as BRST cohomology.
Later the ghosts were reinterpreted as generators of the Chevalley-Eilenberg
complex for Lie algebra cohomology. Cohomological physics also makes use of
group theoretic cohomology, algebraic deformation theory and especially a novel
extension of homological algebra, combining Lie algebra cohomology with the
Koszul-Tate resolution, the major emphasis of the talk. This synergistic
combination of both kinds of cohomology appeared in the
Batalin-Fradkin-Vilkovisky approach to the cohomological reduction of
constrained Poisson algebras. An analogous `odd' version was developed in the
Batalin-Vilkovisky approach to quantizing particle Lagrangians and Lagrangians
of string field theory. A revisionist view of the Batalin- Vilkovisky machinery
recognizes parts of it as a reconstruction of homological algebra with some
powerful new ideas undreamt of in that discipline.
