This book is ideally suited for a two-term, undergraduate algebra course culminating in Galois theory. It gives an introduction to group theory and to ring theory en route. In addition, the chapter on groups, including applications to error-correcting codes and to solving the Rubik's cube, is suitable for a one-term course. The book's concise style is intended to foster student-instructor discussion, as is the selection of exercises of various levels of difficulty.