Group Theory: Definitions and Properties

This lecture covers the fundamental concepts of group theory, including injective, surjective, and bijective functions, as well as the properties of groups such as associativity, the existence of a neutral element, and inverses. It also introduces abstract groups, commutativity, and examples of groups like integers under addition and permutations. The lecture concludes with propositions on involutivity, uniqueness of the neutral element, and uniqueness of inverses in a group.