Differential geometry studies the local and global properties of curved spaces. Topics of the lecture will be: curves and surfaces in Euclidean space, differentiable manifolds, vector bundles, especially the tangent bundle, tensors, Riemannian manifolds, connections, curvature tensors, the geometry of submanifolds, geodesics, and some theorems from global differential geometry.

Basic linear algebra, basic calculus.

W. Kühnel, Differential Geometry: Curves - Surfaces - Manifolds, Oxford University Press. in German: Differentialgeometrie: Kurven - Flächen - Mannigfaltigkeiten, Vieweg Verlag. M. P. doCarmo, Differential Geometry of Curves and Surfaces, Prentice Hall. in German: Differentialgeometrie von Kurven und Flächen, Vieweg Verlag. J.-H. Eschenburg, J. Jost, Differentialgeometrie und Minimalflächen, Springer Verlag. A. Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, CRC Press. in German: Differentialgeometrie. Klassische Theorie in moderner Darstellung, Spektrum Verlag. D. Hilbert, S. Cohn-Vossen, Geometry and the Imagination, Oxford University Press. in German: Anschauliche Geometrie, Springer Verlag. S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer Th. Bröcker, K. Jänich, Einführung in die Differentialtopologie, Springer Ch. Bär, Elementare Differentialgeometrie, de Gruyter W. Blaschke, Vorlesungen über Differentialgeometrie, Springer E. Brieskorn, H. Knörrer, Ebene algebraische Kurven, Birkhäuser