How Set-Valued Maps Pop Up in Control TheoryH.FrankowskaauthorWe describe four instances where set-valued maps intervene either as a tool to state the results or as a technical tool of the proof. The paper is composed of four rather independent sections: (1) Set-Valued Optimal Synthesis and Differential Inclusions; (2) Viability Kernel; (3) Nonsmooth Solutions to Hamilton-Jacobi-Bellman Equations; (4) Interior and Boundary of Reachable Sets.1996-12WP-96-116Monograph