Nonlinear phenomena are abundant in nature and lead to a wealth of open problems in both mechanics and control theory. The classical theory and methods in Nonlinear Mechanics have been developed for mechanical systems with an assumed differentiability of force laws and motion. The presence of unilateral constraints, stemming from frictional contact, is therefore usually not considered or treated in an ad-hoc way. The development of rigorous modeling, simulation and analysis techniques for mechanical systems with unilateral constraints has recently become an emerging topic in scientific and engineering research. The Institute for Nonlinear Mechanics aims to conduct fundamental research on nonlinear mechanical systems using both theoretical and experimental methods. Our research is not specialized to a subfield in Nonlinear Mechanics or limited to a certain application field. At the same time, our research has a clear focus on nonsmooth mechanical systems. Our goal is to push the envelope of fundamental research in Nonlinear Mechanics towards a general theory for nonsmooth mechanical systems, thereby forming an embedding for the existent framework of classical mechanics. Hereto, we use and develop theory and methods from nonsmooth analysis, differential geometry, stability theory and variational analysis. Below you find the topics on which we are currently working, each of them shaping a cornerstone for a more general theory of mechanics.