In this unit introduces permutation groups. It covers the symmetric and alternating groups, and conjugacy in symmetric groups. Cayley's Theorem, which asserts that every finite group is isomorphic to a permutation group, is discussed, illustrated and proved.One subsection is intended to be studied in conjunction with an audio, available in the Group Theory A Block Pack (order code M208/MMPGTA). The video programme, Cayley's Theorem, associated with this unit is available on DVD00094 (order code M208/DVD01).