The recently discovered occurrence of multiple divergences in the irreducible vertex functions of strongly correlated electron models, poses serious problems to the state-of-the-art many-body theory. Dynamical mean-field theory (DMFT) calculations for the Hubbard model have shown several lines of divergences of the irreducible vertex function, surrounding the Mott-Hubbard metal-insulator transition, a clear hint of a highly non-perturbative origin. At high temperatures/large interaction (U), where the Hubbard model approaches the atomic limit, the divergences could be ascribed to a unique underlying energy scale . This simple picture is however not applicable in the most interesting parameter regime of low temperatures and intermediate U, where the system behaves like a correlated Fermi-liquid metal. For this reason a simpler model was analysed, where a similar physics could be realized: the Anderson impurity model. ^This provides a more feasible way to treat the Fermi-liquid quasiparticle physics in the parameter regime of interest. In a preceding Projektarbeit I performed CT-HYB calculations at the two particle level, using w2dynamics. The results show the first divergence line for the Anderson impurity model, with an unexpected low temperature behaviour. Motivated by these preliminary findings, in this thesis an investigation of the whole phase diagram of the Anderson impurity model has been per- formed. In particular, using w2dynamics, additional lines of divergences were found: They could be classified in terms of the properties of their associated singular eigenvectors and compared with the corresponding ones found in other many-electron systems. ^This information provides novel insights on the physical mechanism underlying the breakdown of many-body perturbation theory, clarifying some aspects (such as the relation of the divergences with the Mott-Hubbard transition), which were not fully understood yet. In the final part of the master thesis the implication of the low-temperature behaviour of the divergence lines in the Anderson impurity model onto other models (such as the Hubbard) is discussed as well.