This book presents group theory to students taking a course to transition to advanced mathematics. The goal is to prepare these students for higher level mathematical study, including advanced algebra courses. The book covers the usual material which is found in a first course on groups. The first three chapters are preliminary. Chapter 4 establishes a number of results about integers which will be used freely in the remainder of the book. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups and groups of residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem.