Finite simple groups are a special class of mathematical structures 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 themselves. They play a crucial role in the classification of all finite groups, as every finite group can be broken down into simple groups. The classification of finite simple groups is a monumental achievement in mathematics, completed in the late 20th century. This classification includes several families of groups, such as cyclic groups, alternating groups, and Lie groups, along with numerous sporadic groups. Understanding these groups helps mathematicians explore symmetry and structure in various mathematical contexts.