Symmetry plays an important role in geometry and topology and can best be treated in systematic fashion through introduction of the theory of groups. The existence and classification of finite groups of symmetries of manifolds of dimensions less than five will be studied, with particular emphasis on group actions on four-dimensional manifolds. Here breakthroughs by S. Donaldson and M. Freedman in recent years have produced powerful new methods that opened up a host of formerly inaccessible problems.
