The Royal Society of Edinburgh is Scotland's national academy of science and letters. The membership consists of over 1400 peer-elected fellows, who are known as Fellows of the Royal Society of Edinburgh, denoted FRSE in official titles. It provides annual grants totalling over half a million pounds for research and entrepreneurship. The Society organises public lectures and promotes the sciences in schools throughout Scotland.
It covers a broader selection of fields than the affiliated Royal Society of London including literature and history.

Awards
Fellows of the Royal Society of Edinburgh, denoted by the use of the initialism FRSE in official titles, have included:

Alexander Aitken, New Zealand mathematician
Jack Allen, Canadian physicist who helped discover the superfluid phase of matter in 1937 using liquid helium, Professor of Physics at the University of St Andrews
Sir William Eric Kinloch Anderson, Provost of Eton College
John Arbuthnott, 16th Viscount of Arbuthnott, Scottish soldier and businessman
Struther Arnott, Scottish molecular biologist and Vice-chancellor of the University of St Andrews
Robert Bald, surveyor and mining engineer
Sir Derek Barton, chemist, winner of the Nobel Prize for Chemistry
Sir James W. Black, Scottish pharmacologist who invented Propranolol, synthesised Cimetidine, and received the Nobel Prize for Medicine in 1988
Robert Black, Queen's Counsel, Professor of Scots Law at the University of Edinburgh
Norman Borlaug, American agricultural scientist, winner of the Nobel Peace Prize in 1970, father of the Green Revolution
Sarah Broadie, philosopher specialising in metaphysics and ethics, Professor of Moral Philosophy at the University of St Andrews
John Campbell Brown, Astronomer Royal for Scotland, Regius Professor of Astronomy at the University of Glasgow
Sir Samuel Brown, engineer and suspension bridge pioneer
Sir Kenneth Calman, Scottish doctor, Chief Medical Officer for Scotland then England, Vice-chancellor of Durham University; Chancellor of Glasgow University
Roger Cowley, physicist, Professorof Experimental Philosophy at Oxford
Cyril Offord
Tom Devine
Kenneth Dover
Professor Sir David Edward
James Alfred Ewing, Scottish physicist and engineer, discoverer of hysteresis, Vice-chancellor of the University of Edinburgh
Ian Fells
John Fincham
James David Forbes
Alexander Gray, Scottish economist, translator and poet, Professor of Political Economy at the University of Aberdeen and the University of Edinburgh
William Michael Herbert Greaves
John Currie Gunn
James E. Talmage, Geologist, Chemist, prolific author (see Jesus the Christ (book)), President of the University of Utah, Apostle of The Church of Jesus Christ of Latter-day Saints
Peter Higgs
Right Reverend Richard Holloway, writer, broadcaster, Bishop of Edinburgh in the Scottish Episcopal Church
James Hutton, regarded as the founder of modern geology
John Mackintosh Howie
John Jamieson
Fleeming Jenkin
Mstislav Keldysh
Cargill Gilston Knott
Brian Lang, Scottish anthropologist, Vice-chancellor of the University of St Andrews
Chris J. Leaver, Professor of Plant Sciences at the University of Oxford
Sir Neil MacCormick, Regius Professor of Public Law at the University of Edinburgh and Vice-president of the Scottish National Party
Neil Mackie, Scottish tenor, Head of Vocal Studies at the Royal College of Music
Aubrey Manning, English zoologist and broadcaster, Professor of Natural History at the University of Edinburgh
James Napier, Scottish writer
John Playfair, Scottish mathematician and physicist, Professor of Mathematics and the Natural Philosophy at the University of Edinburgh
Lyon Playfair, 1st Baron Playfair
Juda Hirsch Quastel
John Randall, physicist
Muir Russell
Sir Walter Scott, romantic and historical novelist (Ivanhoe, Rob Roy, The Lady of the Lake, Waverley, The Heart of Midlothian and others)
Richard Sillitto
John Sinclair, writer
Adam Smith, classical economist; philosopher of the Scottish Enlightenment
Alexander McCall Smith, Rhodesia-born Scottish novelist (The No. 1 Ladies' Detective Agency, Portuguese Irregular Verbs, The Sunday Philosophy Club, 44 Scotland Street and others), Professor of Medical Law at the University of Edinburgh
Christopher Smout
Stewart Sutherland, Baron Sutherland of Houndwood, Scottish Academic who served as the Vice-Chancellor and Principle for the University of Edinburgh
Peter Guthrie Tait
George Thomson, Baron Thomson of Monifieth, Labour Party minister and European Commissioner
William Thomson, 1st Baron Kelvin, Irish-Scottish mathematical physicist and engineer
Ronald Pearson Tripp, paleontologist
Colin Vincent
Conrad Hal Waddington
James Watt, Scottish inventor and engineer whose improvements to the steam engine were fundamental to the Industrial Revolution
John Wishart (statistician)
Charles W. J. Withers
Ronald Selby Wright, minister of the Canongate Kirk, Edinburgh
Crispin Wright
Hideki Yukawa, Japanese theoretical physicist who predicted the pion and K-capture, the first Japanese to win a Nobel Prize