Manifolds with special geometric structures play a prominent role in string theory. For example it is well known that supersymmetry requires various target spaces (for sigma models, scalar fields in supergravity theories, etc.) to have certain special geometric properties. In many cases these requirements have interpretation as restrictions on the holonomy group of the Riemannian target space metric. However, in some cases, they cannot be expressed in terms of the Riemannian holonomy group alone and give rise to new geometries previously unknown to mathematicians. The aim of this workshop, held under the auspices of the DFG (German Science Foundation) priority programme in String Theory , is to bring together physicists and mathematicians with the aim of promoting dialogue across the interdisciplinary boundary.