A permutation group is a mathematical concept in group theory that consists of a set of permutations of a given set, along with the operation of composition. A permutation is a rearrangement of elements in a set, and a group is a collection of elements that can be combined in a specific way while satisfying certain properties, such as closure, associativity, identity, and invertibility. In a permutation group, the elements are the different ways to arrange the set, and the group operation is the process of applying one permutation after another. The study of permutation groups is essential in various fields, including combinatorics, algebra, and geometry, as they help in understanding symmetries and structures within mathematical systems.