The aim of this programme is to bring together researchers in pure and applied mathematics in order to expand and deepen our understanding of infinite-dimensional manifolds and their Riemannian geometry, with special emphasis on those manifolds, which are used in shape analysis, image matching and computational anatomy. The manifolds of interest include the spaces of plane and space curves, the space of immersed surfaces and more generally spaces of mappings between finite-dimensional manifolds. A special case, that is interesting in its own right, is the diffeomorphism group, the space of invertible maps of a manifold to itself. In the field of computational anatomy the diffeomorphism group plays a central role. The space of medical images is acted upon by the diffeomorphism group and differences between images are encoded by diffeomorphisms. The development of robust numerical and statistical methods for analysing medical images is a challenging problem, with geometry being an integral part.