The theory of orders has been variously described as a form of non-commutative arithmetic or non-commutative algebraic geometry. Examples of orders include group rings over rings of integers in the arithmetic case, and Azumaya algebras in the geometric case. In this short course, we will primarily be interested in looking at non-commutative analogues of Dedekind domains.
The course should be accessible to anyone who knows basic algebra (you will be fine if you know the ext functor). Notes will be typed up by Boris Lerner.