This chapter introduces the fundamental concepts and properties of functions. It defines the mode Function and the graph of a function, which is identical to the function itself. Key concepts discussed include the domain and range of a function, the identity function, function composition, injective functions, inverse functions, and restrictions of functions. The chapter also defines the image and inverse image of sets under a function. Several propositions are provided to establish basic facts about these concepts, including the relationship between the graph, domain, and range of a function, and the properties of injective functions and their inverses. The chapter concludes with schemes and propositions that further explore the properties of functions, such as the composition of functions, the restriction of functions, and the inverse of functions.This chapter introduces the fundamental concepts and properties of functions. It defines the mode Function and the graph of a function, which is identical to the function itself. Key concepts discussed include the domain and range of a function, the identity function, function composition, injective functions, inverse functions, and restrictions of functions. The chapter also defines the image and inverse image of sets under a function. Several propositions are provided to establish basic facts about these concepts, including the relationship between the graph, domain, and range of a function, and the properties of injective functions and their inverses. The chapter concludes with schemes and propositions that further explore the properties of functions, such as the composition of functions, the restriction of functions, and the inverse of functions.