Algebra. Noncommutative ring theory. Applications of associative algebras to group theory, Lie groups and algebras and to projective geometry. Infinite dimensional algebras, nil rings, primitive rings, prime rings, domains, algebraic algebras. The Jacobson radical and nil radical. Polynomial rings, matrix rings over noncommutative rings. Algebras with finite Gelfand-Kirillov dimension. Centers and extended centers (extended centroids) of algebras with finite Gelfand-Kirillov dimension. Golod-Shafarevich algebras. Algebras with polynomial, exponential and subexponential growth.