The book is a monograph on one sided serial rings with chain conditions. The author is one of the contributors to this area of research. The book is intended for beginning graduate students, Every attempt has been made so that any student with a background of algebra being taught at undergraduate level can understand the book. First two chapters of the book have been devoted to preliminaries on ring theory. There is a chapter on the construction of certain indecomposable modules, these constructions play a central role in the book.