The American Revolution: Map of the Thirteen Colonies and the Revolutionary War

By the 1760s Britain ruled thirteen colonies along the Atlantic coast, from New Hampshire to Georgia, home to about 2.5 million people, a fifth of them enslaved Africans. Each had its own elected assembly and was used to running its own affairs. Britain's victory over France in the Seven Years' War (1756–1763), known in America as the French and Indian War, removed the French from Canada and the Ohio country; press 1763 to see British North America at its largest.

Victory left Britain with a huge debt and a long frontier to defend. To avoid more wars with Native nations, the Royal Proclamation of 1763 banned settlement west of the Appalachian watershed, the dashed line on the map, angering land-hungry colonists. Parliament then decided the colonies should help pay for their own defence.

The Stamp Act of 1765, a tax on printed paper, provoked riots, boycotts of British goods and a colonial congress; the colonists argued that only their own assemblies, not a Parliament in which they had no members, could tax them. Parliament repealed it but insisted on its right to legislate for the colonies, and new duties followed in 1767. In Boston, British troops fired on a crowd in the Boston Massacre of 5 March 1770, killing five.

When the Tea Act of 1773 gave the East India Company a monopoly, the Sons of Liberty dumped 342 chests of tea into Boston Harbor on 16 December 1773. Parliament replied with the Coercive Acts, which colonists called the Intolerable Acts: it closed the port of Boston and took away Massachusetts's self-government. In September 1774 delegates from twelve colonies met in Philadelphia as the First Continental Congress, and militias began drilling and storing weapons.

On 19 April 1775 General Thomas Gage sent soldiers from Boston to seize militia weapons at Concord. Shots were exchanged on Lexington green at dawn, the "shot heard round the world", and on the march back thousands of militiamen harried the British redcoats all the way to Boston, which they then besieged. On 17 June the British took Breed's Hill and Bunker Hill above the city, but at the cost of over a thousand casualties.

The Second Continental Congress made George Washington commander of a new Continental Army. An American invasion of Canada failed before Quebec on 31 December 1775, but Washington's cannon, dragged from Fort Ticonderoga, forced the British to leave Boston in March 1776.

In January 1776 Thomas Paine's pamphlet Common Sense sold tens of thousands of copies, arguing for complete independence and a republic. Congress voted for independence on 2 July 1776 and on 4 July adopted the Declaration of Independence, drafted mainly by Thomas Jefferson. It announced that "all men are created equal" with rights to "Life, Liberty and the pursuit of Happiness", listed the colonists' grievances against King George III, and declared the colonies "Free and Independent States". The map starts drawing the United States from 1776.

The British struck back with the largest force they had ever sent overseas. General William Howe beat Washington on Long Island in August 1776 and took New York City, which stayed in British hands until 1783. Washington retreated across New Jersey, but on the night of 25–26 December 1776 he crossed the icy Delaware River and surprised the Hessian garrison at Trenton, then won again at Princeton on 3 January 1777.

In 1777 Howe captured the rebel capital, Philadelphia, after beating Washington at Brandywine. But a second British army under John Burgoyne, marching south from Canada down the Hudson valley, was surrounded at Saratoga and surrendered on 17 October 1777. It was the turning point of the war: France signed an alliance with the United States in February 1778, Spain joined the war against Britain in 1779 and the Dutch in 1780. Washington's army survived a hard winter at Valley Forge and emerged trained by the Prussian officer Baron von Steuben.

Stalemated in the north, the British turned south, hoping Loyalists would rise to support them. They took Savannah in December 1778 and Charleston in May 1780, capturing over 5,000 American troops, and crushed another army at Camden. But a bitter partisan war followed. Frontier militia destroyed a Loyalist force at Kings Mountain in October 1780, and at Cowpens in January 1781 Daniel Morgan routed Banastre Tarleton's legion. Lord Cornwallis won at Guilford Courthouse in March but lost a quarter of his army, and he marched north into Virginia.

In the summer of 1781 Washington and the French general Rochambeau marched their armies from New York to Virginia, while a French fleet under the Comte de Grasse beat the Royal Navy at the Battle of the Chesapeake on 5 September and cut Cornwallis off from the sea. Besieged at Yorktown by about 17,000 American and French troops, Cornwallis surrendered his army of about 8,000 men on 19 October 1781. In Britain the government fell, and peace talks began.

In the Treaty of Paris, signed on 3 September 1783, Britain recognised the independence of the United States, with a western border on the Mississippi River and a northern border through the Great Lakes, far larger than the thirteen colonies; compare 1775 and 1783 on the map. Britain returned Florida to Spain, its ally France gained little but debt, and Spain kept Louisiana west of the Mississippi.

Tens of thousands of Loyalists left for Canada, Britain and the Caribbean, and thousands of enslaved people who had joined the British in return for freedom left with them. Native nations, most of whom had sided with Britain, were not even mentioned in the treaty, and lost their lands to the expanding republic. After the weak Articles of Confederation, the new nation wrote the Constitution in 1787, and George Washington became its first president in 1789.