The third annual CRM Summer School took place in Banff (Alberta, Canada) and was aimed toward advanced students and recent PhDs. This volume presents surveys from the group theory part of the theme year and examines different approaches to the topic: a geometric approach, an approach using methods from logic, and an approach with roots in the Bass-Serre theory of groups acting on trees. The work offers a concise introduction to current directions of research in combinatorial group theory. Surveys in the text are by leading researchers in the field who are experienced expositors. The text is suitable for use in a graduate course in geometric and combinatorial group theory.
Some open problems by G. Baumslag Length functions and $\Lambda$-trees by I. M. Chiswell Introduction to hyperbolic and automatic groups by S. M. Gersten Description of fully residually free groups and irreducible affine varieties over a free group by O. Kharlampovich and A. Myasnikov Homological methods in group theory by Y. Kuz'min Pro-$p$ groups by M. du Sautoy Identities of representations of finite groups by S. M. Vovsi.