Preface -- Part I Mathematical and Physical Underpinnings of Spacetimes -- Figures of Light in the Early History of Relativity (1905-1914) -- The Behaviour of Rods and Clocks in General Relativity and the Meaning of the Metric Field -- Hilbert on General Covariance and Causality -- Part II Testing General Relativity and Rival Theories -- Putting General Relativity to the Test: Twentieth Century Highlights and Twenty-First Century Prospects -- Rotating Hollow and Full Spheres: Einsein, Thirring, Lense, and Beyond -- Relativistic Lighthouses: The Role of the Binary Pulsar in Proving the Existence of Gravitational Waves -- The Rise and Fall of the Fifth Force -- Part III Geometry and Cosmology, Past and Present -- Cyclic Models of the Relativistic Universe: The Early History -- Inflation and the Origins of Structure -- Problems with Modified Theories of Gravity, as Alternatives to Dark Energy -- The Unexpected Resurgence of Weyl Geometry in Late 20th-Century Physics -- Part IV Mathematical Motifs in General Relativity and Beyond -- Matter from Space -- The Surprising Resolution of the Poincarén Conjecture -- Unified Field Theory up to the 1960s: Its Development and Some Interactions Among Research Groups -- Part V Quantum Gravity, Conformal Boundaries, and String Theory -- The Formulation of Quantum Field Theory in Curved Spacetime -- Conformal Infinity - Development and Applications -- String Theory and Spacetime Geometry -- Conference Program.