Axiomatic Set Theory is a branch of mathematical logic that focuses on the study of sets, which are collections of objects. It is based on a set of axioms, or fundamental principles, that define how sets behave and interact. These axioms provide a foundation for understanding various mathematical concepts and help avoid paradoxes that can arise from naive set definitions. One of the most well-known systems of Axiomatic Set Theory is the Zermelo-Fraenkel Set Theory (ZF), often combined with the Axiom of Choice (AC), forming ZFC. This framework allows mathematicians to rigorously explore the properties of sets, including operations like union, intersection, and power sets, while ensuring consistency and clarity in mathematical reasoning.