This report will survey some points of connection between Hermitian I algebraic K-theory and geometric topology.The earlier and important links between topology and algebraic K-theory (see [MI]) and the more recent links with higher algebraic K-groups (see the papers of Hatcher, Wa ~oner, and Hsiang-Sharpe in these proceedings) will not be discussed systematically. Indications of and/or references to known (to me) or announced calculations of Wall groups (up to December 1972) will be given, together with occasional and brief indications of important topological applications, where these exist. Of course, the works referred to often give fuller descriptions than is possible here.I Karoubi convinoed me that this name is better than "unitary K-theory".