A companion volume to ""Graduate Algebra: Commutative View"", this book presents a unified approach to many important topics, such as group theory, ring theory, Lie algebras, and gives conceptual proofs of many basic results of noncommutative algebra.

The structure of rings: Fundamental concepts in ring theory Semisimple modules and rings and the Wedderburn-Artin theorem The Jacobson program applied to left Artinian rings Noetherian rings and the role of prime rings Algebras in terms of generators and relations Tensor products Exercises-Part IV Representations of groups and Lie algebras: Group representations and group algebras Characters of finite groups Lie algebras and other nonassociative algebras Dynkin diagrams (Coxeter-Dynkin graphs and Coxeter groups) Exercises-Part V Representable algebras: Polynomial identities and representable algebras Central simple algebras and the Brauer group Homological algebra and categories of modules Hopf algebras Exercises-Part VI Bibliography Index.