Abraham Adrian Albert was one of the 20th century's leading mathematicians. This 1937 monograph written by him was hailed by the Bulletin of the American Mathematical Society as "a welcome addition to the literature." Besides furnishing an excellent introduction to abstract algebra and a detailed commentary on then-recent developments, the treatment's important features include chapters on matrices and matrix algebras, cyclic fields, and valuations. Suitable for students ready to advance beyond introductory courses, this book will also prove of interest to historians of mathematics. Opening chapters focus on groups and rings, rings with a unity element, matrices, similarity of square matrices, and symmetric and skew matrices. Readers are given as much of the theory of finite groups as is necessary for the treatment of Galois theory. Subsequent chapters explore algebraic extensions and the ideas grouped around the theory of valuations. Numerous problems of varying complexity appear throughout the text, which concludes with a helpful glossary offering brief definitions of frequently used terms. AUTHOR: Abraham Adrian Albert (1905-72) was an American mathematician primarily known for his groundbreaking work on algebra. In this book, which was originally published in 1938, Albert provides a detailed exposition of 'modern abstract algebra', taking into account numerous discoveries in the field during the preceding ten years.