TU Berlin Fakultät II
Institut für Mathematik

Geometry I



Geometry Group







Geometry I (Winter 2022 / 2023)

Lectures Alexander Bobenko Mon 12-14 MA 144
Fri 12-14 MA 043
Tutorials Jan Techter Wed 14-16 MA 749
Fri 14-16 MA 549


  • Non-Euclidean Geometries and Klein's Erlangen program: projective geometry, hyperbolic geometry, Möbius geometry.
  • This is a course of the Berlin Mathematical School held in english.
  • Lecture notes for the course will be published on a weekly basis.
  • In the tutorials we will introduce and use the python library pyddg and rendering software blender.
  • Course registration on ISIS: here.


[2022, October 07]
Please register on the courses ISIS page.
[2022, October 05]
During the second lecture, on October 21, we will present the python library pyddg, and help you with the installation.
If possible to you, please bring a laptop.
[2022, October 05]
First lecture on October 17.
First tutorial on October 26.


  • Hitchin, lecture notes on Projective Geometry: Chapters 1&2 (Intro, Proj. Spaces),   3 (Quadrics),   4 (Exterior Algebra),   5 (Klein's Erlanger Program)
  • Lecture notes by Boris Springborn
  • V. V. Prasolov & V. M. Tikhomirov. Geometry
  • Felix Klein. Vorlesungen über höhere Geometrie, Vorlesungen über nicht-euklidische Geometrie.
  • Wilhelm Blaschke. Projektive Geometrie. Birkhäuser, Basel, 1954.
  • Fuchs & Tabachnikov, Mathematical Omnibus
  • Marcel Berger. Geometry. I & II. Springer-Verlag, Berlin, 1987.
  • Michèle Audin. Geometry. Springer-Verlag, Berlin, 2003.
  • H. S. M. Coxeter. Non-Euclidean Geometry, Projective Geometry.
  • 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.

Jan Techter . 07.10.2022.