The lecture provides an introduction to Differential and Riemannian Geometry.
Here you may find the exercise sheets:
For Metric Geometry see
Burago, Burago, Ivanov, "A course in metric geometry", 2001.
Bridson, Haefliger, "Metric spaces of non-positive curvature", 1999.
For curves, see
Kühnel, "Differential Geometry: Curves - Surfaces - Manifolds", 2006.
Bär, "Elementary Differential Geometry", 2010.
For smooth manifolds, see
Lee, "Introduction to smooth manifolds", 2000.
For Riemannian manifold, see
Gallot, Hulin, Lafontaine, Riemannian Geometry, 2004
Do Carmo, Riemannian Geometry, 1992
Petersen, Riemannian Geometry, 2006