If "M" and "N" are not assumed to be simply connected, then an "h"-cobordism need not be a cylinder. The "s"-cobordism theorem, due independently to Mazur, Stallings, and Barden, explains the general situation: An "h"-cobordism is a cylinder if and only if the Whitehead torsion of the inclusion vanishes. This generalizes the "h"-cobordism theorem because the simple connectedness hypotheses imply that the relevant Whitehead group is trivial. In fact the "s"-cobordism theorem implies that there is a bijective correspondence between isomorphism classes of "h"-cobordisms and elements of the Whitehead group.