Primary Supervisor = N. Stern-Brocot-Br�che, Graphen und die Modulgruppe. In his Diplom thesis, Hendrik Demmer studied the modular group: the quotient of the group SL2 (Z) by its centre. He constructed a cellular model for the action of the modular group, as a bridge between the classical geometrical model - the modular tree of Serre - and Kulkarnis arithmetic model. The latter admits the advantage that for every subgroup of finite index in the modular group, a Farey symbol can be computed in an efficient way, containing the essential information about the group structure. Demmers model is a graph, constituting the 1-skeleton of a two-dimensional cell complex dual to the modular tree. Its set of edges is the set of elements of the modular group itself; and its 0-skeleton is the projective line over the rational numbers, to which Hendrik Demmer lends additional arithmetic structure as the set of Stern-Brocot fractions.