The Meeting is aimed at gathering experts or reseachers with an interest in global Lorentzian geometry under weak regularity assumptions on the metric. A growing number of papers is considering possible generalizations of the spacetime geometric structure. Some of these works consider affine connections which are just Lipschitz, or even metrics which are just continuous; others take inspiration from the methods of Non-regular Riemannian Geometry. Finally, some lines of research are more topological or, being quantum inspired, involve methods from non-commutative geometry. They all might provide new insights into the structure of the spacetime manifold at the metric level and beyond.