Course overview
The geometry of Euclid, flat space geometry, was believed for a long time to be the only geometry possible. In the 19th century examples were produced of curved space geometries, by various authors. Of these, the most far-reaching and general was developed by B. Riemann. This course is a modern introduction to Riemann’s geometry, starting from the notion of smooth manifold, Riemannian metric, connections, geodesics, and curvature. This proved the ideal setting for Einstein’s study of relativity, for instance.