Abstract
This chapter considers the notion of asymptotic dimension. It first provides an overview of asymptotic dimension before explaining the asymptotic dimensions of free abelian and nonabelian groups, free groups, groups, integers, metric spaces, and products. It then looks at the large-scale geometry of a Cayley graph of a finitely generated group, along with the topological notion of dimension and the large-scale notion of dimension. It also analyzes three typical questions that are asked about asymptotic dimension before concluding with some other examples of groups where something is known about their asymptotic dimension, such as braid groups, Artin groups, surface groups, hyperbolic groups, Coxeter groups, Thompson's group, and wreath product. The discussion includes exercises and research projects.
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