The Möbius Function is a mathematical function used in number theory, denoted as μ(n). It assigns values based on the prime factorization of a positive integer n. Specifically, μ(n) equals 1 if n is a square-free positive integer with an even number of distinct prime factors, -1 if n is square-free with an odd number of distinct prime factors, and 0 if n has a squared prime factor. This function plays a crucial role in various areas of mathematics, including the Möbius Inversion Formula and the study of number theory. It helps in understanding the distribution of prime numbers and has applications in combinatorics and algebraic topology.