Alessandra Veratelli: Möbius transformations.
Diplom thesis, Ferrara 1988.
Original title: Le trasformazioni di Moebius.
THE RIEMANN SPHERE

Stereographic projection
Elementary plane geometry in complex form
Elements of projective geometry
The projective line
The double ratio
The function J

MÖBIUS TRANSFORMATIONS

Some elementary constructions
Pencils of circles
Classification of Möbius transformations

AUTOMORPHISMS OF THE COMPLEX PLANE AND OF THE RIEMANN SPHERE

The Casorati-Weierstraß theorem
Automorphisms of the complex plane and of the Riemann sphere

AUTOMORPHISMS OF D AND H

Schwarz's lemma
Automorphisms of the unitary disc
The group SU(1,1)
Automorphisms of the upper half-plane
The hyperbolic metric in the unitary disc
The hyperbolic metric in the upper half-plane

THE MODULAR GROUP

Euclidean algorithm
Continued fractions
Linear diophantine equations
The group SL(2,Z)
Description of SL(2,Z) by continued fractions
The fundamental domain of the modular group

REFERENCES