Totally degenerated formal schemes In this thesis we study the rigid analytic Picard variety for a certain class of higher dimensional rigid analytic varieties over a complete non Archimedean valued field; namely those which have a totally degenerated formal model. These varieties are a natural generalization of the well known Mumford curves into higher dimensions. We show that the Picard variety in this case is given by a quotient of an algebraic torus by a multiplicative lattice a fact which is well known for Mumford curves. In special cases we give a criterion when the Picard variety is proper; i.e. when the lattice has full rank.