For a long time, finite semifields have been studied from a geometric point of view, since they coordinatize certain types of Projective planes. But recent results relating semifields and coding theory (and also the study of generalized Galois rings) have stimulated the study of these rings from a strictly algebraic point of view. In this work we follow the second path, the term semifield is used to describe an algebraic system which satisfies all properties of a field except for commutativity and associativity of multiplication. Semifields are of special interest today because the projective planes constructed from them have rather remarkable properties.