An integral domain is a type of mathematical structure known as a ring that has specific properties. It is a set equipped with two operations, addition and multiplication, where the multiplication is commutative, and there are no zero divisors. This means that if the product of two elements is zero, at least one of those elements must also be zero. Integral domains also contain a multiplicative identity, usually denoted as 1, which is different from the additive identity, 0. Additionally, every non-zero element in an integral domain has a unique factorization into irreducible elements, making it a crucial concept in abstract algebra and number theory.