Books
 J. W. Anderson, Hyperbolic geometry. Easy treatment of the plane hyperbolic geometry. It covers around half of the topics of this seminar.
 H. Meschkowski, NonEuclidean geometry. From histroical and logical point of view. Through parallel postulate.
 S. Katok, Fuchsian groups. We will more or less cover the first four chapters of this book.
 B. Iversen, Hyperbolic geometry. Unfortunately it is out of stock. I have the library's copy. You can borrow it from me.
 A. F. Beardon, The geometry of discrete groups. The first five weeks, we more or less follow this book. Chapters 7, 8, and parts of 9, 10.

DATE 
PRESENTER 
TOPIC 
Sep 23 

Fundamental concepts
Parallel postulate. Different models. Hyperbolic metric.

Sep 30 

Hyperbolic area and trigonometry GaussBonnet, Angle of parallelism, The sine rule, The cosine rule I, II. 
Oct 7 

Polygons Area of a polygon, Convex polygon, Quadrilaterals, Pentagons, Hexagons. 
Oct 14 

The geometry of geodesics Distance from a line, Perpendicular bisector, Common orthogonal of disjoint geodesics, Pencils of geodesics. 
Oct 21 

Geometry of isometries Classification of isometries, Displacement function, Canonical region. 
Nov 4 

Fuchsian groups Discreteness criteria (GDG) or (HG'), Algebraic properties (FG), Elementary Fuchsian groups (FG), Jorgensen inequality (FG). 
Nov 11 

Fundamental domains Drichlet domain, Modular group, Locally finite domain. 
Nov 18 

A work of Siegel Some remarks on discontinuous groups, The Annals of Mathematics, Second Series, Vol. 46, No. 4, (Oct., 1945), pp. 708718. 
Nov 25 

Either study signature of a Fuchsian group, or reserve this time to catch up with the schedule.

Dec 2 

Continued fraction C. Series, The modular surface and continued fractions, J. London Math. Soc. (2), 31 (1985), 6980.

Dec 9 

Uniformization theorem Hyperbolic surface, HopfRinow theorem, Uniformization theorem. (HG') 
Jan ? 

Monodromy theorem Geodesic lifting property, Monodromy theorem. (HG') 
