First-Order Logic (FOL) is a formal system used in mathematics, philosophy, and computer science to express statements about objects and their relationships. It extends propositional logic by allowing the use of quantifiers, such as 'for all' and 'there exists', enabling more complex expressions and reasoning about properties of objects. In FOL, statements can be constructed using predicates, which represent properties or relations, and terms, which refer to objects. This powerful framework allows for rigorous proofs and the formulation of theories, making it essential for fields like artificial intelligence and mathematical logic.