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In this tutorial we present the main ideas of the algebraic approach in the field of the formalization and computer-aided representation of musical structures (Andreatta and Agon, 2003). In this perspective, well-known music-theoretical and analytical paradigms, as American Pitch Class Set Theory (Forte, 1973; Castine, 1994), can be considered as a special case of the mathematical concept of group action and can be easily generalized and implemented in a computer-aided music analysis and composition environment. We show how the change of the group acting on a basic set enables to have different catalogues of musical structures, as well in the pitch as in the rhythmic domain. This enables, for example, the navigation of the user inside of the universe of all possible musical scale in any well-tempered system.