Taught by Professor Eli Aljadeff, Technion University, Israel The main theme of this mini-course is gradings by finite groups on finite-dimensional algebras. Similar to the classical situation of ungraded algebras, we will be interested in finite-dimensional graded simple algebras and finite-dimensional graded division algebras. An important role is played by a generalization of central simple algebras, called Azumaya algebras. Our main tool will be polynomial identities and, in particular, graded polynomial identities. This tool will allow us to construct generic graded…