The Royal Bank of Scotland was founded by royal charter in 1727. Through mergers and natural growth, it has branches throughout not only Scotland, but also England and Wales. It is based in Edinburgh, Scotland, with a spectacular main branch on St Andrews Square.
The Royal Bank is one of the three banks in Scotland authorised to print money (controlled, of course, by the Bank of England). Royal Bank notes, along with those printed by the Bank of Scotland, Clydesdale Bank, and the Bank of England, circulate freely in Scotland. Notes from the Bank of Ireland (in Northern Ireland) turn up from time to time as well. This causes no end of confusion for tourists, who can end up with five different kinds of paper money in their wallets (coins, at least, do not vary within the UK). All these notes are legal tender in England and Wales, but usually require some argument before they're accepted.
In March 2000, the Royal Bank acquired the much larger National Westminster Bank and renamed itself the Royal Bank of Scotland Group. Because of the acquisition, it has become the largest bank in the UK.