  A monoid hypersurface is an irreducible hypersurface of degree d which has a
singular point of multiplicity d-1. Any monoid hypersurface admits a rational
parameterization, hence is of potential interest in computer aided geometric
design. We study properties of monoids in general and of monoid surfaces in
particular. The main results include a description of the possible real forms
of the singularities on a monoid surface other than the (d-1)-uple point. These
results are applied to the classification of singularities on quartic monoid
surfaces, complementing earlier work on the subject.
