Contents: Introduction; Curves; Gauss Curvature; Surfaces in E3; First Fundamental Form; Second Fundamental Form; The Gauss Curvature in Detail; Geodesics; The Curvature Tensor and the Theorema Egregium; Manifolds; Special Relativity: The Geometry of Flat Spacetime; Inertial Frames of Reference. The Michelson Morley Experiment. The Postulates of Relativity. Relativity of Simltaneity; Coordinates; Invariance of the Interval; The Lorentz Transformation; Spacetime Diagrams; Lorentz Geometry; The Twin Paradox; Temporal order and Causality; General Relativity: The Geometry of Curved Spacetime; The Principle of Equivalence ; Gravity as Spacetime Curvature; The Consequences of Einstein\'s Theory; Geodesics; The Field Equations; The Schwarzschild Solution; Orbits in General Relativity; The Bending of Light. |