A simple group is a type of mathematical structure in the field of group theory, which is a branch of abstract algebra. A group is considered simple if it has no nontrivial normal subgroups, meaning its only normal subgroups are the trivial group and the group itself. This property makes simple groups fundamental building blocks in the study of all groups, similar to how prime numbers are the building blocks of integers. Simple groups can be classified into two main categories: finite simple groups and infinite simple groups. The classification of finite simple groups is a significant achievement in mathematics, revealing a rich structure that includes groups like the alternating groups and the groups of Lie type. Understanding simple groups helps mathematicians explore more complex group structures and their applications in various fields, including physics, cryptography, and combinatorics.