These are the lecture notes from a rather crowded one-term course I gave at Yale University in the spring of 1967. My aim at that time was to give a self-contained account of certain classification theorems in the field of permutation groups. These are theorems which are frequently quoted and yet are reasonably inaccessible. In particular I refer to the work of Zassenhaus on Frobenius complements and sharply transitive groups, and to the work of Huppert on solvable doubly transitive groups. The students were assumed to be familiar with elementary group theory, linear algebra, and Galois theory, or in other words with material covered in a basic course in modern algebra.