**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Several models of the hyperbolic space: the upper-half space
model and the Poincaré disc model.
- Hyperbolic distance, area and geodesics.
- The Möbius group: action of
on the hyperbolic space.
- Classifying different types of isometries.
- Hyperbolic triangles, hyperbolic trigonometry, hyperbolic polygons.
- Fuchsian groups: discrete subgroups of
.
- Fundamental domains and Dirichlet regions.
- Limit sets. Elementary and non-elementary Fuchsian groups.
- Poincaré's theorem and groups generated by side-pairing transformations.

- S. Katok, Fuchsian Groups, Chicago Lectures in Mathematics, University of Chicago
Press.
- J. Anderson, Hyperbolic Geometry, Springer Undergraduate Mathematics Series,
Springer-Verlag, 1999.
- Alan F. Beardon, The Geometry Of Discrete Groups, Graduate Texts in Mathematics 91,
Springer-Verlag, 1983.
- John G. Ratcliffe, Foundation Of Hyperbolic manifolds, Graduate Texts in Mathematics 149, Springer-Verlag, 1994