Law officers edit

• Lord Advocate – James Montgomery
• Solicitor General for Scotland – Henry Dundas

Judiciary edit

• Lord President of the Court of Session – Lord Arniston, the younger
• Lord Justice General – Duke of Queensberry
• Lord Justice Clerk – Lord Barskimming

• 27 June – foundation stone of General Register House in Edinburgh, designed by Robert Adam, is laid; the building will not be opened until 1788.^[1]
• Dundas House in New Town, Edinburgh, designed by William Chambers, is completed.
• Punitive laws against the Clan Gregor are repealed.^[2]
• Roman Catholic chapel built on the site that will become St Peter's Church, Aberdeen.
• The Schiehallion experiment is carried by Nevil Maskelyne out to determine the mean density of the Earth.^[3]

• 24 February – Archibald Constable, publisher (died 1827)
• 26 February – William Farquhar, soldier and administrator in the East India Company (died 1839)
• 3 June – Robert Tannahill, weaver poet (died 1810)
• 8 October – Henry Duncan, (Free) Church of Scotland minister, geologist and social reformer; founder of the savings bank movement (died 1846)
• 4 November – Robert Allan, weaver poet (died 1841 in New York)
• 8 November – Robert Reid, royal architect (died 1856)
• 12 November – Charles Bell, anatomist (died 1842 in England)
• 24 November – Thomas Dick, Secession Church minister and scientist (died 1857)
• Robert Thom, hydraulic engineer (died 1847)

• 19 January – Thomas Gillespie, Presbyterian minister (born 1708)
• 16 October – Robert Fergusson, Scottish poet (born 1750; died in bedlam following head injury)

• During this year's harvest, 15-year-old farm labourer Robert Burns is assisted by his contemporary Nelly Kilpatrick who inspires his first attempt at poetry, "O, Once I Lov'd A Bonnie Lass".

• Musselburgh Golf Club established on Levenhall Links and the Old Club Cup is played for the first time.

• Timeline of Scottish history