Groups in stable and simple theories

These are sketch notes for my lecture on the MALOA Introductory Day of the meeting ‘Geometric Model theory’, March 25–28 2010, Oxford. They were written after the lecture, but have not been carefully polished. The bibliography is not carefully put together. For an old but wonderful introduction to stable group theory, see [13]. For an update, often with results stated in great generality, see [15]. On groups of finite Morley rank, [2] gives the state of play prior to serious intrusion of methods from the classification of finite simple groups, and [1] gives close-to-current information.