This book on modern module and non-commutative ring theory starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. The first half of the book is concerned with free, projective, and injective modules, tensor algebras, simple modules and primitive rings, the Jacobson radical, and subdirect products. Later in the book, more advanced topics, such as hereditary rings, categories and functors, flat modules, and purity are introduced. These later chapters will also prove a useful reference for researchers in non-commutative ring theory.