Which Roman emperor built the great wall across northern Britain?

Hadrian, from AD 122 - 117 kilometres coast to coast, with a fort every Roman mile, turrets between them and a ditch on each side. It took about six years and was built by the legions themselves, which is what a professional army does when there is no war on.

It was probably not primarily a defensive line. It is too long to man against a serious assault and too permeable, with gates at every mile; the better reading is a customs and control barrier - regulating who crossed, taxing what they carried, and making a visible statement about where the empire stopped. Hadrian's policy generally was consolidation rather than conquest, and a wall is that policy rendered in stone.

It is also not the Scottish border and never was, running entirely within England and some way south of the line. The Antonine Wall was pushed further north twenty years later, held for about eight years, and was abandoned. What survives is largely the middle sections in open country - the rest was quarried for centuries, and a substantial stretch went into eighteenth-century military roads built to move troops against Jacobite risings, which is a wall being demolished to build a road for the same purpose.