Stable homotopy is the branch of homotopy theory that studies phenomena that remain "constant" after applying the suspension functor a sufficient amount of times. For example one can show that the homotopy groups of the -sphere are independent of , if is sufficiently big. These groups take the name of stable homotopy groups of spheres, and computing them turns out to be a very difficult problem. I will introduce these notions, and then say something about the tools that can be used to attempt to compute the stable homotopy groups of spheres.

Some knowledge in homotopy theory (fundamental group, or maybe homotopy groups) can be useful for understanding the talk, but I will try to introduce what I need.