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This self-contained monograph describes basic set-theoretic methods for control and provides a discussion of their links to fundamental problems in Lyapunov stability analysis and stabilization, optimal control, control under constraints, persistent disturbance rejection, and uncertain systems analysis and synthesis. New computer technology has catalyzed a resurgence of research in this area, particularly in the development of set-theoretic techniques, many of which are computationally demanding. The work presents several established and potentially new applications, along with numerical examples and case studies. A key theme of the presentation is the trade-off between exact (but computationally intensive) and approximate (but conservative) solutions to problems.