Abstract. Multidimensional databases are large collections of data, often historical, used for sophisticated analysis oriented to decision making. This activity is supported by an emerging category of software technology, called On-Line Analytical Processing OLAP. In spite of a lot of commercial tools already available, a fundamental study for OLAP systems is still lacking. In this paper we introduce a model and a query language to establish a theoretical basis for multi-dimensional data. The model is based on the notions of dimension and f-table. Dimensions are linguistic categories corresponding to di erent ways of looking at the information. F-tables are the constructs used to represent factual data, and are the logical counterpart of multi-dimensional arrays, the way in which current analytical tools store data. The query language is a calculus for f-tables, and as such it o ers a high-level support to multi-dimensional data analysis. Scalar and aggregate functions can be embedde...