We discuss the nature of the semantics of the UML. Contrary to the case of most languages, this task is far from trivial. Indeed, not only the UML notation is complex and its informal description is incomplete and ambiguous, but we also have the UML multiview aspect to take into account. We propose a general schema of the semantics of the UML, where the different kinds of diagrams within a UML model are given individual semantics and then such semantics are composed to get the semantics on the overall model. Moreover, we fill part of such a schema, by using the algebraic language Casl as a metalanguage to describe the semantics of class diagrams, state machines and the complete UML formal systems.