During the second half of the Twentieth Century, algebraic methods have been increasingly recognised as powerful approaches to the formalisation of musical structures. This library is entirely based on the algebraic properties of the finite cyclic group Z/nZ (shortly Zn) and some relevant music applications. The tutorial is divided in two parts. In the first one cyclic groups are applied to the rhythmic domain, according to the model of periodic rhythm developed by the Rumanian mathematician Dan Tudor Vuza. In particular we focused on the problem of construction of rhythmic canons having the property of tiling musical time space. In the second part, cyclic groups are applied to the pitch domain in order to show how some basic algebraic properties share a musically pertinent dimension. The main inspiration source has been the theoretical work of the Rumanian composer Anatol Vieru.