Data abstractions were originally conceived as a specification tool in programming. They also appear to be useful for exploring and explaining the capabilities and shortcomings of the data definition and manipulation facilities of present-day database systems. Moreover they may lead to new approaches to the design of these facilities. In the first section the paper introduces an axiomatic method for specifying data abstractions and, on that basis, gives precise meaning to familiar notions such as data model, data type, and database schema. In a second step the various possibilities for specifying data types within a given data model are examined and illustrated. It is shown that data types prescribe the individual operations that are allowed within a database. Finally, some additions to the method are discussed which permit the formulation of interrelationships between arbitrary operations.