The Jacobi Symbol is a mathematical notation used in number theory, particularly in the study of quadratic residues. It is denoted as \left(\fracan\right), where a is an integer and n is an odd positive integer. The Jacobi Symbol generalizes the Legendre Symbol, allowing for a wider range of values for n, which can be any odd integer, not just a prime. The Jacobi Symbol can take values of -1, 0, or 1, indicating whether a is a quadratic residue modulo n. It is computed using properties of prime factorization and multiplicative properties, making it useful in algorithms for cryptography and primality testing.