  We introduce the notion of cyclic cohomology of an A-infinity algebra and
show that the deformations of an A-infinity algebra which preserve an invariant
inner product are classified by this cohomology. We use this result to
construct some cycles on the moduli space of algebraic curves. The paper also
contains a review of some well known notions and results about Hochschild and
cyclic cohomology of associative algebras, A-infinity algebras, and deformation
theory of algebras, and includes a discussion of the homology of the graph
complex of metric ribbon graphs which is associated to the moduli space of
Riemann surfaces with marked points.
