Set-valued analysis is the study of set-valued maps (multifunctions) and has wide applications in various fields. It combines elements of topology, measure theory, and nonlinear functional analysis, and is closely related to nonsmooth analysis. The development of set-valued analysis is closely linked to nonsmooth analysis, and today it is a mature field with many applications in social sciences, biology, and engineering. This chapter presents the basic aspects of set-valued maps, focusing on those necessary for important applications like optimization, optimal control, game theory, and mathematical economics. The chapter is structured as follows: Section 4.1 examines the topological aspects of set-valued maps, introducing continuity concepts. Section 4.2 explores measure-theoretic aspects, introducing measurability concepts. Section 4.3 discusses the existence of measurable selections for multifunctions, presenting the Kuratowski-Ryll Nardzewski and Yankov-von Neumann-Aumann selection theorems. Section 4.4 considers continuous selections, with the Michael Selection Theorem as a key result. Section 4.5 introduces decomposable sets, which are essential for defining set-valued integrals. Section 4.6 presents a set-valued integral and its topological variant. Section 4.7 examines modes of convergence for sets and their applications to sequences of functions and multifunctions. Notations are provided for various classes of subsets of topological and normed spaces. The chapter uses standard notation for neighborhoods, balls, and distances in topological and metric spaces.Set-valued analysis is the study of set-valued maps (multifunctions) and has wide applications in various fields. It combines elements of topology, measure theory, and nonlinear functional analysis, and is closely related to nonsmooth analysis. The development of set-valued analysis is closely linked to nonsmooth analysis, and today it is a mature field with many applications in social sciences, biology, and engineering. This chapter presents the basic aspects of set-valued maps, focusing on those necessary for important applications like optimization, optimal control, game theory, and mathematical economics. The chapter is structured as follows: Section 4.1 examines the topological aspects of set-valued maps, introducing continuity concepts. Section 4.2 explores measure-theoretic aspects, introducing measurability concepts. Section 4.3 discusses the existence of measurable selections for multifunctions, presenting the Kuratowski-Ryll Nardzewski and Yankov-von Neumann-Aumann selection theorems. Section 4.4 considers continuous selections, with the Michael Selection Theorem as a key result. Section 4.5 introduces decomposable sets, which are essential for defining set-valued integrals. Section 4.6 presents a set-valued integral and its topological variant. Section 4.7 examines modes of convergence for sets and their applications to sequences of functions and multifunctions. Notations are provided for various classes of subsets of topological and normed spaces. The chapter uses standard notation for neighborhoods, balls, and distances in topological and metric spaces.