The lecture focusses on Metric, Differential and Riemannian Geometry.
Tutorials are given by Bogdan Georgiev. Note that the tutorials start on Monday, October 24th, 2016. (As usual, the lecture starts in the first week of the semester, i.e. on Tuesday, October 18th.)
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 smooth manifolds, see
Lee, "Introduction to smooth manifolds", 2000.
For Riemannian manifolds, see
Lee, "Riemannian manifolds - and introduction to curvature", 1997
Gallot, "Hulin, Lafontaine, Riemannian Geometry", 2004
Do Carmo, "Riemannian Geometry", 1992
Petersen, "Riemannian Geometry", 2006