The main goal of our SFB project is to investigate the interplay of interactions and spin-orbit coupling for strongly correlated electron systems in one and two spatial dimensions. We intend to analyze interaction effects for one-dimensional systems with potentially emergent topology, such as helical edge state models of topological insulators as well as spin-orbit coupled quantum wires and ladders. To a large extent, these systems are investigated jointly with experimental groups within ToCoTronics. We pursue this direction with a set of different methods including density matrix renormalization group (DMRG), exact diagonalization, bosonization, and equations-of-motion approaches. Passing from correlated spin-orbit electron models in one to two spatial dimensions, it becomes more relevant to resolve the interdependencies between conventional electronic order and topological aspects of the electronic scenario. In order to analyze unconventional, frustrated magnetism in spin-orbit Mott insulators, our SFB project research agenda is to study the infinite coupling limit of spin-orbit electronic systems described by multi-orbital Hubbard models. We employ the pseudo-fermion functional renormalization group (FRG) method to compute magnetic susceptibilities for large finite size realizations. The perspective of spin-orbit Mott physics is complemented by investigations of spin-orbit Fermi liquids in weak coupling, where the spin-orbit coupling can have a profound effect on the Fermiology yielding e.g. possible topological superconducting states of matter. We intend to extend the Fermi surface FRG to generalized Rashba spin-orbit scenarios with unprecedented phenomenology for electronically-mediated superconductors. Moreover, we wish to devise efficient formulations for the two-dimensional surface states of three-dimensional topological insulators that are amenable to numerical solution via exact diagonalization.