The Scottish Enlightenment was a period of intellectual ferment in Scotland, running from approximately 1740 to 1800.
In the period following the 1707 Act of Union, Scotland's place in the world changed radically. Arguably the poorest and most backward country in western Europe in 1700, it was thrown into the economic and cultural deep-end of the British Empire. Under this stimulus, Scottish thinkers began questioning everything; with Scotland's traditional connections to France, then in the throes of the Enlightenment, the Scots began developing a uniquely practical branch of humanism.
The first major figure of the Scottish Enlightenment was Francis Hutcheson, who held the Chair of Philosophy at the University of Glasgow from 1729 to 1746. A moral philosopher in opposition to the ideas of Thomas Hobbes, he founded one of the major branches of Scottish thinking, that opposed to Hobbes' disciple David Hume. Hutcheson's major contribution to world thought was the utilitarian principle that virtue was that which brought the greatest good to the most people.
Hume himself was arguably the most important person in the Scottish Enlightenment, whose moral thinking eventually largely swamped Hutcheson's, and whose economic work inspired his friend (and the other serious candidate for "most important person"), Adam Smith. Hume was largely responsible for giving the Scottish Enlightenment its practical hue, for he was concerned with the nature of knowledge, and developed ideas related to evidence, experience, and causation. Much of what is incorporated in the scientific method, and many modern attitudes towards the relationship between science and religion, were developed by him.
If Hume was primarily concerned with philosophy and worked less in economics, his ideas nevertheless led to important work in the latter field. Picking up on Hume's championing of free trade, Adam Smith developed the concept and published arguably the first modern economic work -- The Wealth of Nations -- in 1776. This highly influential work had an immediate impact on British economic policy, and its inheritors still inform the 21st century discussions on globalization and tariffs.
Over time, the Scottish Enlightenment shifted focus from intellectual and economic matters to those more specifically scientific. The harbinger of these was James Anderson, a doctor with an abiding interest in agronomy. While the Scottish Enlightenment is traditionally considered to have ended with this change (which occurred at the tail end of the 18th century), it is worth noting that disproportionately large Scottish contributions to British science and culture continued for another fifty years or so, including such figures as James Hutton, James Watt, James Clerk Maxwell, and Sir Walter Scott.