This concise text is geared toward students of mathematics who have completed a basic college course in algebra. Combining material on ring structure and homological algebra, the treatment offers advanced undergraduate and graduate students practice in the techniques of both areas.After a brief review of basic concepts, the text proceeds to an examination of ring structure, with particular attention to the structure of semisimple rings with minimum condition. Subsequent chapters develop certain elementary homological theories, introducing the functor Ext and exploring the various projective dimensions, global dimension, and duality theory. Each chapter concludes with a set of exercises.