With last meeting's discussion of the Freudenthal Suspension Theorem in mind, we turn to a natural question: what structure of homotopy groups remains stable after repeated applications of the suspension functor? Let X and Y be CW complexes of finite type, the stable homotopy classes of maps [Y,X] form a finitely generated abelian group and the Adams spectral sequence allows one to calculate its p-torsion from the knowledge of the (reduced) cohomology groups H*(X,F_p) and H*(Y,F_p). We will first have to understand the properties of these cohomology groups considered as modules over a Steenrod algebra and why this is natural from a "stable" point of view. Spectra and spectral sequences will also be introduced in the discussion, and we will look an application to the 2-torsion of stable homotopy groups of spheres.