Where did the name Britannia come from?

The Romans referred to the imperial province as Britannia, which eventually comprised all of the island of Great Britain south of the fluid frontier with Caledonia (Scotland). Before the Roman invasion, begun in AD 43, Iron Age Britain already had established cultural and economic links with Continental Europe, but the Roman invaders introduced new developments in agriculture, urbanization, industry and architecture. Besides the native British record of the initial Roman invasion, Roman historians generally mention Britannia only in passing. Thus, most knowledge of Roman Britain has derived from archaeological investigations, and the epigraphic evidence lauding the Britannic achievements of an Emperor of Rome, such as Hadrian (r. AD 117–38) and Antoninus Pius (r. AD 138–61), whose walls demarcated the northern borders of Roman Britain.