**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Free Groups: groups defined by generators and relations, the graph of a group.
- Factor groups and subgroups: word groups, reduced free groups, presentations, subgroups of a free group.
- Nielsen transformations: Reduction process, automorphisms of free groups.
- Free products and amalgamation: Universal property of a product. Categorical definitions. HNN extensions.
- Commutator calculus. Lower central series. Lie elements. Baker-Hausdorff formula.

- Discrete subgroups of Lie groups.
- Mapping Class groups.
- Groups and Trees.

- W. Magnus, A. Karrass, D. Solitar Combinatorial Group Theory, Dover Books on Mathematics, 2004.
- R. C. Lyndon, P. E. Schupp, Combinatorial Group Theory, Classics in Mathematics, Springer, 1977.
- D. J. S. Robinson, A course in the Theory of Groups, Graduate Texts in Mathematics 80, Springer-Verlag, 1995.

- M. S. Raghunathan, Discrete Subgroups of a Lie Group, Springer Verlag.
- J. Birman, Mapping Class groups, Princeton University Press.
- J. P. Serre, Trees, Wiley Press.