Geometrical Structures on Space-Time -- Light Rays and Light Cones -- Local Structure and Topology -- Homogeneity Properties -- Ordered Spaces and Complete Uniformizability -- Spaces with Complete Light Rays -- Consequences of Order Completeness -- The Cushion Problem -- Related Works -- Concluding Remarks -- Erratum to: Geometrical Structures on Space-Time -- Erratum to: Light Rays and Light Cones -- Erratum to: Local Structure and Topology -- Erratum to: Ordered Spaces and Complete Uniformizability -- Erratum to: Spaces with Complete Light Rays -- Erratum to: Consequences of Order Completeness -- Erratum.

The present work is the first systematic attempt at answering the following fundamental question: what mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The authors propose an axiomatization of Einstein-Weyl causality (inspired by physics), and investigate the topological and uniform structures that it implies. Their final result is that a causal space is densely embedded in one that is locally a differentiable manifold. The mathematical level required of the reader is that of the graduate student in mathematical physics.