Gorenstein orders

After a survey of basic characterizations and properties of one-dimensional Gorenstein rings we consider the classical orders in algebraic number fields in a very general setup. We point out connections between Gorenstein properties and properties of orders first introduced by Dedekind and Noether. Some results going back to Dedekind–Noether–Grell are slightly extended and presented in a more modern/homological language.In the final sections particular emphasis is on explicit families and examples of Gorenstein orders and the number of generators for ideals.