When studying semigroups and monoids the nonexistence of an inverse element yields new challenges. Semigroup

theory saw a major development in the second half of the 20th century being one of its celebrated results the

Eilenberg’s Variety Theorem which relates varieties of finite monoids to varieties of formal languages. In this

seminar we present an extension of this result to formations of finite monoids and some classes of languages,

followed by an application to saturated formations of groups.