Judge and politician. The son of another Robert Dundas (1713 - 1787) and the sixth in a line of remarkable lawyers and politicians. Called to the bar in 1779, Dundas was appointed Solicitor General for Scotland in 1784. By 1789 he was Lord Advocate for Scotland and was Lord Chief Baron of Exchequer for Scotland in 1801. He also served for a time as Member of Parliament for Midlothian. With his father, he was a founding fellow of the Royal Society of Edinburgh in 1783.
Dundas married his cousin, Elizabeth, the daughter of Henry Dundas, Viscount Melville (1742 - 1811). His son, another Robert, was the last of the line to be active in the law.