Zermelo's Well-Ordering Theorem states that every set can be well-ordered, meaning that its elements can be arranged in a sequence where every non-empty subset has a least element. This theorem is significant in set theory and is foundational for various mathematical concepts, including ordinal numbers and transfinite induction. The theorem is named after the mathematician Ernst Zermelo, who proved it in the early 20th century. It relies on the Axiom of Choice, a controversial principle in mathematics that asserts the ability to select elements from sets. Well-ordering is essential for understanding the structure of infinite sets and their properties.