  The parameter coclass has been used successfully in the study of nilpotent
algebraic objects of different kinds. In this paper a definition of coclass for
nilpotent semigroups is introduced and semigroups of coclass 0, 1, and 2 are
classified. Presentations for all such semigroups and formulae for their
numbers are obtained. The classification is provided up to isomorphism as well
as up to isomorphism or anti-isomorphism. Commutative and self-dual semigroups
are identified within the classification.
