  This is an expanded and updated version of a talk given at the Conference on
Topics in Geometry and Physics at the University of Southern California,
November 6, 1992. It is a survey talk, aimed at mathematicians AND physicists,
which attempts to bring together the topics in the title without assuming much
background in any of them. Closed string field theory leads to a (strong
homotopy) generalization of Lie algebra, which is strongly related to the way
the moduli spaces $\Cal M_{0,N+1}$ fit together as an ``operad''. The latter in
turn plays an important role in the understanding of vertex operator algebras.

High Energy Physics - Theory