Electronic properties of solids are analyzed and computed in Metzner's department with a main emphasis on systems where electronic correlations play a crucial role, such as cuprates and other transition metal oxides. Besides symmetry-breaking phase transitions leading to magnetism, orbital and charge order, or superconductivity, correlations can also cause electron localization and many other striking many-body effects not described by the independent electron approximation. Our research focuses in particular on high-temperature superconductors with their complex interplay of magnetic, superconducting and charge correlations, and also on manganites, titanates, and vanadates, whose electronic properties are determined by the interplay of orbital, spin and charge degrees of freedom. Besides bulk properties of one-, two- and three-dimensional systems, also surface states of topological phases, as well as problems with a mesoscopic length scale such as quantum dots, quantum wires, and quantum Hall systems are being studied. The correlation problem is attacked with various numerical and field-theoretical techniques: exact diagonalization, density matrix renormalization group, dynamical mean-field theory and functional renormalization group. Modern many-body methods are not only being applied, but also further developed within our group.