Within project C02 we systematically studied the interaction of magnetic adatoms with normal-metallic or superconducting substrates . To establish a solid foundation we initially reinvestigated the properties of vortices on clean and oxygen-reconstructed Nb(110) surfaces. This STS study revealed an unexpected vortex anisotropy for clean Nb(110). In collaboration with project B05 this anisotropy could be traced back to the Fermi surface and the resulting shape of Caroli-de Gennes-Matricon states. Oxidizing the Nb(110) surface triggers the transition from the clean to the dirty limit, attenuates the vortex bound states, and leads to an isotropic appearance of the vortices. In the light of above observations it can be rationalized that the Yu-Shiba-Rusinov (YSR) states formed by single Fe atoms on Nb(110) also depend on the cleanliness of the surface. In cooperation with project B06 and C07, our STS results showed an intriguing correlation between the quantum phase transition of YSR states in the superconducting state and a Kondo screening in the normal metallic state. Furthermore, we studied the hybridization of YSR states of magnetic adatom chains on superconducting surfaces. We observe a splitting of the single-atom YSR peaks into multiple states with even or odd spatial symmetry and identified a peculiar dependence of the even and odd states’ energy position on the chain length . In the second funding period we developed a novel technique that combines ultra-high spatial with improved spectroscopic resolution by STM tips which are at the same time functionalized by CO and Nb, see Sect. 3.4.2. In the next funding period we will use this expertise to engineer and scrutinize the properties of (i) two-dimensional thin film hybrid systems, (ii) one-dimensional adatom chains, and (iii) lattices of impurities, which are viable platforms to realize topological superconductors hosting the Majorana modes. Towards (i) we will study thin films of either heavy elements with strong spin-orbit coupling, such as Bi and Pb, or topological insulators, such as Bi2Te3 (collaboration with A01). We will utilize the proximity-induced superconductivity effect and study bound states of surface Dirac fermions trapped in vortex cores. To increase the parameter space available for 3d transition metal and 4f rare-earth metal adatoms and chains in (ii), we will fine-tune the exchange coupling of the adatoms to the superconducting substrate by ultra-thin insulating layers, e.g. NaCl. Here, we will continue our successful cooperation with projects B03, B05, B06, and C07. Finally, we will investigate if and how (iii) the construction of suitable quantum-mechanical interference devices will allow for a long-range coupling between Shiba impurities, a feature highly favorable for the realization of YSR- qubits.