This Proceedings presents refereed versions of most of the papers presented at the NATO Advanced Research Institute on Homotopy Methods and Global Convergence held in Porto Cervo, Sardinia, June 3-6, 1981. This represents the fourth recent occurrence of an international conference addressing the common theme of fixed point computation. The first such conference, ti tled "Computing Fixed Points with Applications," was held in the Department of Mathematical Sciences at Clemson University, Clemson, South Carolina, June 26-28, 1974 and was sponsored by the Office of Naval Research and the Office...