The main way of coping with the complexity of software systems is to construct and use models expressed in UML. Unfortunately, the semantics (meaning) of models written in UML is not precisely defined. It may result in the incorrect interpretation of a model and make it hard to strictly verify a model and its transformation. In this paper we formally (mathematically) define UML class diagram and its semantics. The problem of consistency of the diagram is then introduced and some examples of inconsistencies are forwarded.