This chapter introduces the theory of set-valued maps, also known as multifunctions, which is a significant branch of mathematics with applications in various fields such as social and economic sciences, biological sciences, and engineering. The theory combines elements from point-set topology, measure theory, and nonlinear functional analysis, and is closely related to nonsmooth analysis. The chapter covers the basic aspects of set-valued maps, focusing on their topological and measure-theoretic properties, including continuity, measurability, and selection theorems. Key topics include the Kuratowski-Ryll Nardzewski selection theorem, the Yankov-von Neumann-Aumann selection theorem, the Michael Selection Theorem, and the concept of decomposable sets. The chapter also discusses set-valued integrals and modes of convergence for sequences of functions and multifunctions. Throughout, the chapter uses specific notations for different types of sets in topological and normed spaces, and conventions for neighborhoods and balls in metric spaces.This chapter introduces the theory of set-valued maps, also known as multifunctions, which is a significant branch of mathematics with applications in various fields such as social and economic sciences, biological sciences, and engineering. The theory combines elements from point-set topology, measure theory, and nonlinear functional analysis, and is closely related to nonsmooth analysis. The chapter covers the basic aspects of set-valued maps, focusing on their topological and measure-theoretic properties, including continuity, measurability, and selection theorems. Key topics include the Kuratowski-Ryll Nardzewski selection theorem, the Yankov-von Neumann-Aumann selection theorem, the Michael Selection Theorem, and the concept of decomposable sets. The chapter also discusses set-valued integrals and modes of convergence for sequences of functions and multifunctions. Throughout, the chapter uses specific notations for different types of sets in topological and normed spaces, and conventions for neighborhoods and balls in metric spaces.