The Alexander polynomial is a mathematical invariant used in the field of knot theory, which studies the properties of knots and links. It is a polynomial that helps distinguish different knots by providing a way to classify them based on their topological features. The polynomial is derived from a knot's presentation and can be computed using various methods, including the use of a Seifert surface. Introduced by James W. Alexander in 1928, the Alexander polynomial is defined for a knot or link in three-dimensional space. It is expressed as a polynomial in one variable, typically denoted as t , and can reveal important information about the knot's structure, such as its genus and whether it is a prime knot.