The semi-stable homotopy groups of a topological space [italic]X are the unstable homotopy groups [lowercase Greek]Pi [subscript]*[capital Greek]Sigma[superscript]n[italic]X, [italic]n [greater than symbol] 0, of the suspensions of [italic]X. This monograph is concerned with computing these semi-stable homotopy groups using the unstable Adams spectral sequence for the free iterated loop spaces [capital Greek]Omega[superscript italic]n [capital Greek]Sigma[superscript italic]n [italic]X generated by [italic]X.