Understanding the stability of edge and surface states under the breaking of different symmetries or in the presence of disorder and their relation to high-energy anomalies is at the heart of this SFB 1170 proposal. In the first funding period, we investigated new magnetism-related effects, such as the tunneling planar Hall effect in ferromagnet/topological insulator junctions, as well as the forma- tion and stability of edge states in nodal semimetals. Based on this experience, in the second funding period, we will focus on different types of evolution of topologically protected metallic states in topolog- ical insulators and Dirac semimetals. We will investigate how the surface states of Dirac semimetals evolve under applied strain, bulk inversion asymmetry terms (Weyl semimetals) and electron-electron interactions. The central question will be not only to trace the evolution of surface states under dif- ferent perturbations, but also to derive the most general boundary conditions for a given symmetry class to understand deeper the bulk-boundary correspondence. Concerning the role of disorder, we have an expertise in calculating quantum transport in topological materials in the presence of non- magnetic as well as magnetic impurities. In the second period, on the one hand, we will study the evolution/destruction of surface states and Fermi arcs by magnetic impurities. On the other hand,we will study the quantum anomalous Hall (QAH) effect in strictly (2+1)-dimensions, which is char- acterized by an insulating gap and a single chiral edge state at the boundary. The origin of the QAH effect is due to an exchange field resulting from multiple magnetic impurities. Further, since the QAH effect is characterized by a non-zero Chern number without Landau levels, this effect is related to the parity anomaly in (2+1)-dimensions. Here, we will answer the central question how this high-energy anomaly (parity anomaly) changes different transport regimes (hydrodynamical, ballistic and diffusive regimes) for the QAH effect and will study the evolution of QAH edge states in out-of-plane magnetic fields (orbital fields).