The GAP 4 Package MONOID 3.1.4. IMPORTANT UPDATE 2011: the monoid package has been superseded by the Citrus package for GAP 4.5. Consequently, monoid is no longer maintained and we recommend you use Citrus instead. MONOID 3.1.4 retains all the functionality of the original MONOID package. In particular, MONOID 3.1.4 contains more efficient methods than those available in the GAP library for computing orbits, calculating Green’s classes, finding the size, the elements, and testing membership in transformation semigroups. After MONOID has been loaded many of these methods are automatically used in preference to those in the library and do not need to be called explicitly by the user. In addition, there are new methods for testing if a semigroup satisfies a particular property, such as if it is regular, simple, inverse, or completely regular; computing the automorphism group of a transformation semigroup; homomorphisms and isomorphism between some types of semigroup; and functions to create some well-known transformation semigroups. The MONOID package is written in GAP code only but uses the GRAPE and orb packages.