Zermelo-Fraenkel Set Theory (ZF) is a foundational system for mathematics that describes how sets, which are collections of objects, can be constructed and manipulated. It consists of a series of axioms that define the properties and relationships of sets, ensuring consistency and avoiding paradoxes. One of the key features of ZF is the Axiom of Choice, which allows for the selection of elements from sets in a systematic way. Together, ZF and the Axiom of Choice (often referred to as ZFC) provide a robust framework for much of modern mathematics, enabling the study of various mathematical structures and concepts.