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Faceted classification allows one to model applications with complex classification hierarchies using orthogonal dimensions. Recent work has examined the use of faceted classification for browsing and search. In this paper, we go further by developing a general query language, called the entity algebra, for hierarchically classified data. The entity algebra is compositional, with query inputs and outputs being sets of entities. Our language has linear data complexity in terms of space and quadratic data complexity in terms of time. We compare the expressive power of the entity algebra with relational algebra. We also describe an end-to-end query system based on the language in the context of an archeological database.