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Ordinary theta-functions can be considered as holomorphic sections of line bundles over tori. We show that one can define generalized theta-functions as holomorphic elements of modules over noncommutative tori (theta-vectors). The theory of these new objects is not only more general, but also much simpler than the theory of ordinary theta-functions. I'll not assume any knowledge of noncommutative geometry and of the theory of theta-functions in my talk.