An isomorphism is a mathematical concept that describes a structure-preserving mapping between two objects, such as sets, groups, or spaces. When two structures are isomorphic, they can be considered essentially the same because there is a one-to-one correspondence between their elements that maintains the operations and relations of the structures. In group theory, for example, an isomorphism between two groups means that their operations correspond in a way that preserves the group structure. This concept is important in various fields of mathematics, including algebra, topology, and category theory, as it helps identify when different mathematical objects can be treated as equivalent.