Coarse geometry is the study of metric spaces from a “large scale” point of view, so that two spaces that look the same from a great distance are actually equivalent. Typical examples of spaces are non-compact complete Riemannian manifolds, countable discrete groups, certain graphs and dynamical systems, etc.. This point of view is effective since it is often true that the relevant geometric properties of metric spaces are determined by their coarse structures. In this lecture, we will discuss some basic ideas and examples in coarse geometry, their applications to C^*-algebras and higher index problems, together with some connections to geometric group theory, expander graphs and Banach space geometry.

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