The History of Combinatorial Group Theory

I The Beginning of Combinatorial Group Theory.- I.I Introduction to Part I.- I.2 The Foundations: Dyck's Group-Theoretical Studies.- I.3 The Origin: The Theory of Discontinuous Groups.- I.4 Motivation: The Fundamental Groups of Topological Spaces.- I.5 The Graphical Representation of Groups.- I.6 Precursors of Later Developments.- A. Arithmetically Defined Linear Groups in Higher Dimensions.- B. Arithmetically Defined Linear Groups in Two Dimensions.- C. Geometric Constructions. Fuchsian Groups.- D. Braid Groups and Mapping Class Groups.- E. Differential Equations, Linear Groups, and Lie Groups.- F. Finite Groups.- I.7 Summary.- I.8 Modes of Communication. Growth and Distribution of Research in Group Theory.- I.9 Biographical Notes.- I.10 Notes on Terminology and Definitions.- I.11 Sources.- II The Emergence of Combinatorial Group Theory as an Independent Field.- II. 1 Introduction to Part II.- II.2 Free Groups and Their Automorphisms.- II.3 The Reidemeister-Schreier Method.- II.4 Free Products and Free Products with Amalgamations.- II.5 One-Relator Groups.- II.6 Metabelian Groups and Related Topics.- A. The Principal Ideal Theorem.- B. Applications to the Theory of Knots and Links.- C. A Problem from the Foundations of Geometry.- D. Notes on Later Developments and Generalizations.- II.7 Commutator Calculus and the Lower Central Series.- II.8 Varieties of Groups.- II.9 Topological Properties of Groups and Group Extensions.- II.10 Notes on Special Groups.- II.11 Postscript: The Impact of Mathematical Logic.- II.12 Modes of Communication.- II.13 Geographical Distribution of Research and Effects of Migration.- II.14 Organization of Knowledge.- Index of Names.- Index of Subjects.