TU Berlin Fakultät II
Institut für Mathematik

Geometry I



Geometry Group



Vergangene Semester


Images, Videos, and Games

Virtual Math Labs




Winter Semester 2007/08

Lectures Boris Springborn Tue 12-14 MA 850
Fri 10-12 MA 850
Tutorial A Charles Gunn Wed 10-12 MA 848
Tutorial B Thu 12-14 MA 848

This is a course of the Berlin Mathematical School held in English.

The tutorials will be conducted in two groups. You should choose one.


Please pick up your Übungschein at Frau Gillmeister's office, room MA 320.


Euclidean and non-euclidean geometry: spherical, hyperbolic, projective, Möbius, and Lie geometry. The continuation is Geometry II.

Exercise sheets

Lecuture notes

Downloads and Links

Homework policy

To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments.

In case of heavy correction load, the assistant may choose to correct only a subset of the assigned problems. The 50% requirement refers to the total of the corrected problems.

The homeworks are due weekly at the beginning of the Tuesday lecture (12:15). No homework will be accepted after the deadline has passed.

Homeworks may be turned in directly to the assistant at the lecture, or left with the Sekretariat in MA 3-2 (Room 320).

If you are tempted to copy homework from a classmate, please ask yourself, "What am I learning when I do this?".


Many of the following references can be found in the mathematics library, on reserve for this course. Ask at the desk.
  • V. V. Prasolov & V. M. Tikhomirov. Geometry. Translations of Mathematical Monographs, 200. American Mathematical Society, Providence, RI, 2001.
  • Nigel Hitchin's lecture notes on Projective Geometry.
  • Felix Klein. Vorlesungen über höhere Geometrie. Grundlehren der Mathematischen Wissenschaften, 22. Springer-Verlag, Berlin, 1968.
  • Wilhelm Blaschke. Projektive Geometrie. Birkhäuser, Basel, 1954.
  • Marcel Berger. Geometry. I & II. Springer-Verlag, Berlin, 1987.
  • Michèle Audin. Geometry. Springer-Verlag, Berlin, 2003.
  • H. S. M. Coxeter. Non-Euclidean Geometry. Mathematical Association of America, Washington, DC, 1998.
  • J. W. Cannon, W. J. Floyd, R. Kenyon, R. Parry. Hyperbolic Geometry. In: S. Levy (editor). Flavors of Geometry. Mathematical Sciences Research Institute Publications 31. Cambridge University Press, Cambridge, 1997. Pages 59-115. Download PDF from the MSRI.
  • D. V. Alekseevskij, E. B. Vinberg, A. S. Solodovnikov. Geometry of spaces of constant curvature. In: E. B. Vinberg (editor). Geometry II. Encyclopedia of Mathematical Sciences 29. Springer, Berlin, 1993. Pages 1-138.
(This list is not ordered according to any relevant criteria.)

Office Hours

Office hours Springborn Make Appt. MA 874
Gunn Thursday 16-17:00 MA 319

Boris Springborn . 28.05.2019.