An introduction to equivariant homotopy theory

If G is a topological group, we can make sense of a (continuous) action of G on a space. If X and Y are two spaces equipped with G-actions, an equivariant map f:X-->Y is a map that is compatible with the G-actions on X and Y. We shall explore what it should mean for this to be an equivariant (weak) homotopy equivalence, and we will look at equivariant cohomology theories.