This is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.

1 Sets and Mappings.- 2 The Integers.- 3 Introduction to Rings.- 4 Introduction to Groups.- 5 Rings.- 6 Topics in Group Theory.- Hints to Solutions.- Suggestions for Further Study.