The Banach-Tarski Paradox is a theorem in set theory and mathematics that states it is possible to take a solid ball, divide it into a finite number of non-overlapping pieces, and then reassemble those pieces into two identical solid balls of the same size. This counterintuitive result relies on the properties of infinite sets and the concept of non-measurable sets. The paradox challenges our understanding of volume and geometry, as it suggests that traditional notions of size and quantity do not apply in the same way when dealing with infinite sets. It highlights the complexities of infinity and the foundations of mathematics.