The Axiom of Extensionality is a fundamental principle in set theory, which states that two sets are considered equal if they contain the same elements. In other words, if every element of set A is also an element of set B, and vice versa, then A and B are the same set. This axiom helps to define the concept of sets in a clear and unambiguous way. This axiom is crucial for understanding the nature of sets in mathematics and is part of the foundational framework known as Zermelo-Fraenkel set theory. It emphasizes that the identity of a set is determined solely by its members, rather than any other properties or characteristics.