Algebra

I. Combinatorial Group Theory and Fundamental Groups.- 1. Group Presentations and 2-Complexes.-
1.1. Presentations of Groups.-
1.2. Complexes and Fundamental Groups.-
1.3. Subgroups and Coverings.- 2. Free Groups and Free Products.-
2.1. Free Groups.-
2.2. Amalgamated Free Products and Graphs of Groups.-
2.3. Automorphisms of Free Groups.-
2.4. One-Relator Groups.- 3. Surfaces and Planar Discontinuous Groups.-
3.1. Surfaces.-
3.2. Planar Discontinuous Groups.-
3.3. Subgroups of Planar Groups.-
3.4. Automorphisms of Fuchsian Groups.-
3.5. Relations to Other Theories of Surfaces.- 4. Cancellation Diagrams and Equations Over Groups.-
4.1. Cancellation Diagrams.-
4.2. Locally Indicable Groups and Equations Over Groups.- 5. 3-Manifolds and Knots.-
5.1. Fundamental Groups of 3-Manifolds.-
5.2. Haken Manifolds.-
5.3. On Knots and Their Groups.- 6. Cohomological Methods and Ends.-
6.1. Group Extensions and Cohomology.-
6.2. Ends ofGroups.- 7. Decision Problems.-
7.1. Decision Problems and Algorithms.-
7.2. Unsolvable Decision Problems.-
7.3. Automata and Groups.- Index of Notation.- II. Some Questions of Group Theory Related to Geometry.- 1. Equations in Groups and Some Related Questions.-
1. Basic Concepts and the Theorem of Makanin.-
2. Solutions of Systems and Homomorphisms.-
3. Fundamental Sequences and Razborov's Theorem.- 4. On the Structure of the Set of Solutions of Quadratic Equations in Free Groups.-
5. Coefficient-Free Quadratic Equations.-
6. The Classification of Epimorphisms from Surface Groups to Free Groups.-
7. On the Minimal Number of Fixed Points in the Homotopy Class of Mappings and the Width of Elements in Free Groups.-
8. On Quadratic Equations in Hyperbolic Groups.- 2. Splitting Homomorphisms and Some Problems in Topology.-
1. Heegaard Decompositions of 3-Manifolds and their Equivalence.-
2. The Poincaré Conjecture and Three Algorithmic Problems Connected with 3-Manifolds.-
3. Information on Aut ?1(T) and Some of its

From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996