This course is suggested to students who study noncommutative rings. It gives the fundemantal concepts of noncommutative rings, Applications of Wedderburn’s Theorem, Commutativity theorems,

Simple and primitive rings, The radical of a ring, semisimple Artinian Rings, Semisimple rings, The Density Theorem, Semisimple rings, Simple algebras, The Brauer’s Groups, Maximal subfields, Some classic theorems, Representation of finite groups, polynomial identities, The Goldie’s Theorem, Ultra-products and a theorem of Posner.