Equivalence relations have played a fundamental role through the History of Mathematics. These special relations are so omnipresent in everyday life that we often forget about their proactive existence. Though, according to some authors, still much is unknown about them. In this talk, we will introduce independence and permutability, on the context of a equivalence relations lattice of a given set, refering to the interpretation of these mathematical concepts in the Information Theory point of view. We, then, present the classification of equivalence pairs of finite type, due to B.Jónsson, and introduce the operation star defined within equivalences, restating M.-L. Dubreil fundamental theorem.