This volume reports on research related to Discrete Groups and Geometric Structures, as presented during the International Workshop held May 26-30, 2008, in Kortrijk, Belgium. Readers will benefit from impressive survey papers by John R. Parker on methods to construct and study lattices in complex hyperbolic space and by Ursula Hamenstadt on properties of group actions with a rank-one element on proper CAT (0)-spaces. This volume also contains research papers in the area of group actions and geometric structures, including work on loops on a twice punctured torus, the simplicial volume of products and fiber bundles, the homology of Hantzsche - Wendt groups, rigidity of real Bott towers, circles in groups of smooth circle homeomorphisms, and groups generated by spine reflections admitting crooked fundamental domains.