In s serious of three lectures the speaker will present a survey of results related to the Milnor’s problem on groups growth. It includes the discussion about groups of polynomial growth, groups of exponential growth, and groups of intermediate (between polynomial and exponential) growth.

More generally, the idea of growth for graphs, groups, semigroups, algebras and formal languages will be discussed as well as the question about the analytic properties of the growth series. The construction of groups of intermediate growth will be presented and numerous unusual properties of these groups will be explained. If time permits, also a dual notion of cogrowth will be mention as well as the cogrowth criterion of amenability.

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