This text presents a comprehensive introduction to anextended Entity-Relationship model both on a conceptual andon a formal, mathematicallevel. In addition to theprimitives given by the data model the text introduces alanguage for the formulation of constraints in order torestrict database states to consistent ones. The textexplains an implementation of the approach chosen in thelogic programing language PROLOG and discusses in thiscontext the computational power of the proposedcalculus.The extended Entity-Relationship calculus is used to definethe meaning of the relational query language SQL. A nicefeature of the approach is that it becomes possible to provelanguage properties on a sound mathematical basis.