stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor.

A founding result was the Freudenthal suspension theorem, which states that for a given CW-complex X the (n+i)th homotopy group of its ith iterated suspension, π_{n+i} (Σ^iX), becomes stable (i.e., isomorphic after further iteration) for large but finite values of i.