  Informally, a homotopy monoid is a monoid-like structure in which properties
such as associativity only hold `up to homotopy' in some consistent way. This
short paper comprises a rigorous definition of homotopy monoid and a brief
analysis of some examples. It is a much-abbreviated version of the paper
`Homotopy Algebras for Operads' (math.QA/0002180), and does not assume any
knowledge of operads.
