The Scottish Enlightenment centered on Edinburgh, Glasgow and Aberdeen, and produced from a small and recently impoverished country an outsized share of modern moral philosophy, economics and social theory.
Its distinctive starting point was sociability. Hobbes had begun from isolated individuals calculating advantage. Francis Hutcheson argued instead for a moral sense as native to human beings as sight, and Hume and Smith built on it. Hume grounded morality in sentiment corrected by general points of view. Smith, in The Theory of Moral Sentiments (1759), derived the whole of ethics from sympathy and the internalized judgment of an impartial spectator. His economics is downstream of that moral psychology and not separate from it, which is why reading the Wealth of Nations without it produces a caricature.
The Scots also invented a way of thinking about history. Conjectural or stadial history, in Smith, Ferguson, Kames and Millar, explained institutions as products of successive modes of subsistence instead of legislation or national character, which made law, property and manners into things with a developmental explanation. Ferguson supplied the movement's most quoted line, that establishments arise which are the result of human action but not of human design. Thomas Reid meanwhile mounted the common-sense reply to Hume's skepticism that dominated Anglo-American philosophy for a century.
Its influence traveled unusually well: through the American founders, through nineteenth-century political economy, and through Hayek, who took the anti-rationalist strand as the foundation of his own work. Modern scholarship has been mainly occupied with recovering how much the movement's celebrated commercial optimism was qualified by its own authors, Smith on the stupefying effects of the division of labor and Ferguson on what commercial society does to civic virtue.