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Here by Rome we mean the pope. The western Roman Empire had long fallen by then. The pope asked the Charlemagne, king of the Franks, to attack the Lombards and end their rule in Italy. In exchange, the pope crowned Charlemagne Roman emperor. Italy became part of Charlemagne's empire, which has been called Carolingian empire because it was ruled by Charlemagne's close relatives after his death. Charlemagne also invaded northern Germany and part of Spain. His empire came to cover most of continental western Europe apart from most of the Iberian peninsula, Denmark and Scandinavia, and what was East Germany. Charlemagne was given the title of Roman emperor to symbolise the independence of Italy and the west from the Eastern Roman Empire. Central Italy had been under the control of this empire and the Popes (who were only Bishops of Rome back then) were subordinates of the emperor of the east, even though they had managed to gain considerable autonomy. The alliance with Charlemagne provided the military power for this 'breakaway' from Constantinople.
Maximilian I, and the invaders were the French.
The Germanic peoples who invaded the Western Roman Empire were either already Arian Christians or converted to Roman Catholicism. Emperor Charlemagne conquered norther Germany and sent priests to covert the peoples there to Christianity. Missionaries travelled around the pagan parts of Europe to spread Christianity.
Nadir Shah invaded India to loot India. The Mughal Emperor was Muhammad Shah
Napoleon III (emperor of France) qualifies as such.
Claudius first "invaded" Britain in 43 BC.
Claudius and his entourage "invaded" a mostly pacified Britain in 43 AD.
The Romans called Colchester Colonia Claudia after their emperor that invaded Britain.
It was the Franks. They took over the whole of Gaul at the expense of the Alemanni, Visgoths and Burgundians, who were Germanics who had settled in Gaul. They also took over southern Germany and Switzerland. The Frankish kingdom was turned into the Carolingian empire. The pope asked Charlemagne (king of the Franks) to crush the rule of the Lombards (another Germanic people). In exchange the pope gave him Italy and crowned him emperor. Charlemagne also invaded part of norther Spain. The then invaded northern Germany. His empire covered most of continental western Europe, except for Portugal, most of Spain and Scandinavia.
One reasons that Emperor Claudius invaded Britain was that he wanted to prove himself and secure his thrown. He also wanted to control the trade route.
Kublai Khan was the grand son of Chenghese Khan, a Mongolian Emperor, who invaded India. Kublai Khan invaded China and ruled there for some time.
The first time the Romans invaded Britain was in 55 BC under Julius Caesar. They annexed it as a province in 43 AD under the "invasion" of the emperor Claudius.