On the microscopic theory of interacting bosons

General Theories are discussed, which allow the description of collective excitations in a fermion system in terms of bosonic degrees of freedom. Applications of the Dyson-method in the vicinity of double magic nuclei are presented and the convergence in the number of different bosons is investigated. Using the approximation of one or several broken pairs which is based on a generalized seniority scheme, a method is presented to give a microscopic interpretation of the phenomenological IBA-model. Starting from a microscopic fermion interaction we derive IBA-interaction parameters for spherical nuclei far from closed shells.