Discontinuous Groups of Isometries in the Hyperbolic Plane Book

	Preface
	Life and work of the Authors
I	Mobius transformations and non-euclidean geometry	1
1	Pencils of circles - inversive geometry	1
2	Cross-ratio	4
3	Mobius transformations, direct and reversed	6
4	Invariant points and classification of Mobius transformations	8
5	Complex distance of two pairs of points	14
6	Non-euclidean metric	18
7	Isometric transformations	23
8	Non-euclidean trigonometry	27
9	Products and commutators of motions	43
II	Discontinuous groups of motions and reversions	58
10	The concept of discontinuity	58
11	Groups with invariant points or lines	70
12	A discontinuity theorem	78
13	[actual symbol not reproducible]-groups. Fundamental set and limit set	82
14	The convex domain of an [actual symbol not reproducible]-group. Characteristic and isometric neighbourhood	95
15	Quasi-compactness modulo [actual symbol not reproducible] and finite generation of [actual symbol not reproducible]	115
III	Surfaces associated with discontinuous groups	127
16	The surfaces [actual symbol not reproducible] module [actual symbol not reproducible] and K ([actual symbol not reproducible]) modulo [actual symbol not reproducible]	127
17	Area and type numbers	135
IV	Decompositions groups	153
18	Composition of groups	153
19	Decomposition of groups	174
20	Decompositions of [actual symbol not reproducible]-groups containing reflections	196
21	Elementary groups and elementary surfaces	213
22	Complete decomposition and normal form in the case of quasi-compactness	242
23	Exhaustion in the case of non-quasi-compactness	270
V	Isomorphism and homeomorphism	283
24	Topological and geometrical isomorphism	283
25	Topological and geometrical homeomorphism	308
26	Construction of g-mappings. Metric parameters. Congruent groups	318
	Symbols and definitions	349
	Alphabets	353
	Bibliography	355
	Index	361