  For a pointed topological space $X$, we use an inductive construction of a
simplicial resolution of $X$ by wedges of spheres to construct a "higher
homotopy structure" for $X$ (in terms of chain complexes of spaces). This
structure is then used to define a collection of higher homotopy invariants
which suffice to recover $X$ up to weak equivalence. It can also be used to
distinguish between different maps $f$ from $X$ to $Y$ which induce the same
morphism on homotopy groups $f_*$ from $\pi_* X$ to $\pi_* Y$.
