AUTOMATE, a computing package for automata and finite semigroups. AUTOMATE is a package written in the programming language C that allows to calculate the deterministic non-complete minimal automaton of a rational language and the transition monoid of a deterministic automaton. A library of C-functions dealing with these objects is available as well and is the base of the implementation of AUTOMATE. Languages can be defined either by extended rational expressions or a transition table. Several properties of the transition monoid can be calculated, for example: a list of it’s elements, a set of relations defining the monoid, numbers of regular and idempotent elements, and information about the classes of Green’s relations ℛ, ℒ, ℋ, and the relation 𝒟=ℛ∘ℒ. The main results used for the calculations are presented. Green’s relations are the most powerful tool involved. Finally a long, well commented example run of AUTOMATE is shown in detail.