Hans-Christoph Im Hof's research at the University of Basel focuses on differential geometry, in particular on the structure and symmetry of spaces with non-positive curvature. The focus is on the geometric and topological properties of so-called Riemannian manifolds and the effects of discrete groups on such spaces. With his studies on horospheres, Dirichlet regions and hyperbolic Coxeter groups, he made significant contributions to the understanding of global geometry and its interaction with algebraic structures.