the capital and the smallest state of Austria, in the northeast on the River Danube: seat of the Hapsburgs (1278-1918); residence of the Holy Roman Emperor (1558–1806); withstood sieges by Turks in 1529 and 1683; political and cultural centre in the 18th and 19th centuries, having associations with many composers; university (1365). Pop: 1 752 845 (2015 est). Area: 1075 sq km (415 sq miles)