The notation Aut(G) refers to the group of automorphisms of a mathematical structure G. An automorphism is a bijective mapping from the structure to itself that preserves the operations and relations defined on it. In group theory, for example, G could be a group, and Aut(G) would consist of all the ways to rearrange the elements of G while maintaining the group operation. Aut(G) is important in various fields of mathematics, including algebra and geometry, as it helps to understand the symmetries and structural properties of G. By studying Aut(G), mathematicians can gain insights into how G behaves under different transformations and identify equivalent structures.