We propose a data model and a few algebraic operations that provide semantic foundation to multidimensional databases. The distinguishing feature of the proposed model is the symmetric treatment not only of all dimensions but also measures. The model provides support for multiple hierarchies along each dimension and support for adhoc aggregates. The proposed operators are composable, reorderable, and closed in application. These operators are also minimal in the sense that none can be expressed in terms of others nor can any one be dropped without sacrificing functionality. They make possible the declarative specification and optimization of multidimensional database queries that are currently specified operationally. The operators have been designed to be translated to SQL and can be implemented either on top of a relational database system or within a special purpose multidimensional database engine. In effect, they provide an algebraic application programming interface (API) that allows the separation of the frontend from the backend. Finally, the proposed model provides a framework in which to study multidimensional databases and opens several new research problems.