In this monograph the author presents the theory of duality for nonconvex approximation in normed linear spaces and nonconvex global optimization in locally convex spaces. Detailed proofs of results are given, along with varied illustrations. While many of the results have been published in mathematical journals, this is the first time these results appear in book form. In addition, unpublished results and new proofs are provided. This monograph should be of great interest to experts in this and related fields.