There are several possible notions of a "moduli space" of algebraic structures on an object
(such as a space or spectrum). These notions are homotopy-theoretic, in that they are
homotopy-invariants of the space. We discuss the relationship between these notions
and show how they are related to the problem of realizing a given space (or spectrum) with a given
algebraic structure (such as an A-infinity or E-infinity structure). Time permitting,
we discuss some approaches toward computing these invariants.
Last modified: September 10, 1996