A Dedekind Domain is a special type of integral domain in algebraic number theory. It is defined as a Noetherian integral domain in which every non-zero prime ideal is maximal. This property ensures that the ring has a well-behaved structure, making it easier to study its ideals and their relationships. In a Dedekind Domain, every non-zero element can be factored uniquely into prime elements, similar to how integers can be factored into prime numbers. This unique factorization property is crucial for understanding the arithmetic of algebraic integers, particularly in the context of algebraic number fields and ideal class groups.