Inspired by classical geometry geometric group theory has in turn provided a variety of
applications to geometry topology group theory number theory and graph theory. This
carefully written textbook provides a rigorous introduction to this rapidly evolving field
whose methods have proven to be powerful tools in neighbouring fields such as geometric
topology. Geometric group theory is the study of finitely generated groups via the geometry of
their associated Cayley graphs. It turns out that the essence of the geometry of such groups is
captured in the key notion of quasi-isometry a large-scale version of isometry whose
invariants include growth types curvature conditions boundary constructions and amenability.
This book covers the foundations of quasi-geometry of groups at an advanced undergraduate
level. The subject is illustrated by many elementary examples outlooks on applications as
well as an extensive collection of exercises.
