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