This text presents a comprehensive introduction to an extended Entity-Relationship model both on a conceptual and on a formal, mathematical level. In addition to the primitives given by the data model the text introduces a language for the formulation of constraints in order to restrict database states to consistent ones. The text explains an implementation of the approach chosen in the logic programing language PROLOG and discusses in this context the computational power of the proposed calculus. The extended Entity-Relationship calculus is used to define the meaning of the relational query language SQL. A nice feature of the approach is that it becomes possible to prove language properties on a sound mathematical basis.