Growth of groups

The study and exploitation of connections between group theory and geometry has a long and glorious history. It also forms one of the main areas of ma thematical research at the present day. This particular chapter in that sto ry began in 1968 with seminal work of Milnor relating the curvature of a di fferentiable manifold to the rate of growth of its fundamental group. This article contains a brief survey of developments in the subject since that t ime.