An operad is an abstraction of a family of composable functions of n variables for various n, useful for the “bookkeeping” and applications of such families. Operads are particularly important and useful in categories with a good notion of “homotopy”, where they play a key role in organizing hierarchies of higher homotopies. Operads as such were originally studied as a tool in homotopy theory, but the theory of operads has recently received new inspiration from homological algebra, category theory, algebraic geometry, and mathematical physics, especially string field theory and deformation quantization, as well as new developments in algebraic topology. The name operad and the formal definition appear first in the early 1970s in J. Peter May’s The Geometry of Iterated Loop Spaces, but there is an abundance of prehistory. Particularly noteworthy is the work of Boardman and Vogt.