Carolingian Empire
The size of the empire at its inception was around 1,112,000 square kilometres (429,000 sq mi), with a population of between 10 and 20 million people. Its heartland was Francia, the land between the Loire and the Rhine, where its symbolic capital, Aachen, was located. In the south it crossed the Pyrenees and bordered the Emirate of Córdoba and, after 824, the Kingdom of Pamplona; to the north it bordered the kingdom of the Danes; to the west it had a short land border with Brittany, which was later reduced to a tributary; and to the east it had a long border with the Slavs and the Avars, who were eventually defeated and their land incorporated into the empire. In southern Italy, the Carolingians' claims to authority were disputed by the Byzantines (eastern Romans) and the vestiges of the Lombard kingdom in the Principality of Benevento.
Carolingian Empire-3