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Initially popularized by Amazon.com, recommendation technologies have become widespread over the past several years. However, the types of recommendations available to the users in these recommender systems are typically determined by the vendor and therefore are not flexible. In this paper, we address this problem by presenting the recommendation query language REQUEST that allows users to customize recommendations by formulating them in the ways satisfying personalized needs of the users. REQUEST is based on the multidimensional model of recommender systems that supports additional contextual dimensions besides traditional User and Item dimensions and also OLAP-type aggregation and filtering capabilities. This paper also presents the recommendation algebra RA, shows how REQUEST recommendations can be mapped into this algebra, and analyzes the expressive power of the query language and the algebra. This paper also shows how users can customize their recommendations using REQUEST queries through a series of examples.