Geometric Group Theory: Asymptotic Invariants of Infinite Groups, M. Gromov

This paper is an introduction to certain topics in geometric group theory. We begin with an introduction to Cayley graphs and the word metric. We then move to the notion of quasiisometry, and how this interacts with group actions, making a connection with Riemannian geometry. Following this connection, we examine the growth of balls around the identity, and classify groups by their asymptotic growth type. We focus particularly on groups of exponential growth.