This text covers the traditional approach of groups, rings, fields with the integration of computing and applications found in areas such as coding theory and cryptography. Applied examples are used to aid in the motivation of learning to prove theorems and propositions. The nature of exercises in this text range over several categories including computational, conceptual and theoretical. These exercises and problems allow the exploration of new results and theory. The flexible organization can be used in many different ways to emphasize theory or applications. It includes features and in text learning aids, applications within every chapter, quantity and quality of examples and exercises, supplementary topics, balance of theory and mathematics, historical notes, and computer science projects.