The research at the institute focuses on a variety of topics in combinatorics, graph theory, combinatorial optimization, stochastic models, geometric group theory and non-commutative probability. Complementing our work in pure mathematics, we model, analyse and solve structural and algorithmic problems arising from mathematics, theoretical computer science and natural sciences as well as from applications in industry. More details can be found on the individual websites of the four research groups of the institute: * Combinatorics * Combinatorial Optimization * Structure Theory and Stochastics * Noncommutative Structures The institute is one of the five mathematical institutes of the Faculty of Technical Mathematics and Technical Physics at Graz University of Technology. The institute takes an active part in the Mathematical Doctoral School "Discrete Mathematics" (DK plus programme funded by FWF). Our teaching comprises service courses for the engineering faculties as well as as variety of courses for the studies of Mathematics at our university.