In the lecture, basic topics in Riemannian Geometry are treated from a theoretical point of view and illustrated with several examples.

Content: digest of the following topics:

• Exponential map and HopfRinow theorem
• Riemannian manifolds and metrics, Riemannian curvature tensor
• LeviCivita connection
• Connections between curvature und topology (e.g. Myers theorem, HadamardCartan theorem, Klingenberg theorem, rigidity theorems)
• Closed geodesics
• Stokes theorem, cohomology
• Spaces of constant curvature, Lie groups, symmetric and homogeneous spaces
• Discretization and numerical application

Literature: will be announced in the lecture.