A finite simple group is a type of mathematical structure in group theory, which is a branch of abstract algebra. These groups are defined as nontrivial groups that do not have any normal subgroups other than the trivial group and the group itself. Finite simple groups play a crucial role in the classification of all finite groups, as they serve as the building blocks for more complex group structures. The classification of finite simple groups was a monumental achievement in mathematics, completed in the late 20th century. This classification includes several families of groups, such as the alternating groups A_n, and various groups of Lie type, along with a few exceptional groups. Understanding these groups helps mathematicians explore symmetry and structure in various mathematical contexts.