Symmetry and non Hermiticity in anomalous Floquet topological insulators Festkörperphysik Symmetrie nicht Hermitizität topologische Isolatoren non Hermitian symmetry topological insulators Floquet This thesis contains studies on a special class of topological insulators so called anomalous Floquet topological insulators which exclusively occur in periodically driven systems. At the boundary of an anomalous Floquet topological insulator topologically protected transport occurs even though all of the Floquet bands are topologically trivial. This is in stark contrast to ordinary topological insulators of both static and Floquet type where the topological invariants of the bulk bands completely determine the chiral boundary states via the bulk boundary correspondence. In anomalous Floquet topological insulators the boundary states are instead characterized by bulk invariants that account for the full dynamical evolution of the Floquet system. Here we explore the interplay between topology symmetry and non Hermiticity in two dimensional anomalous Floquet topological insulators. The central results of this exploration are (i) new expressions for the topological invariants of symmetry protected anomalous Floquet topological phases which can be efficiently computed numerically (ii) the construction of a universal driving protocol for symmetry protected anomalous Floquet topological phases and its experimental implementation in photonic waveguide lattices (iii) the discovery of non Hermitian boundary state engineering which provides unprecedented possibilities to control and manipulate the topological transport of anomalous Floquet topological insulators.