Zorn's Lemma is a principle in set theory that states if a partially ordered set has the property that every chain (a totally ordered subset) has an upper bound within the set, then the entire set contains at least one maximal element. A maximal element is one that cannot be exceeded by any other element in the set. This lemma is equivalent to the Axiom of Choice, another fundamental concept in mathematics. Zorn's Lemma is often used in various fields, including algebra and topology, to prove the existence of certain structures, such as bases for vector spaces or maximal ideals in rings.