Abstract: I will attempt to give a gentle introduction to equivariant stable homotopy theory. I will try to explain why, given a G-equivariant space X we care not only about its homotopy groups but about the homotopy groups of the H-fixed points for every subgroup H. Next I will explain why we get transfer maps, but only after suspending by a G-representation sphere. Towards the end I might mention some recent work, time permitting.