Wikijunior:American Founding Fathers/Alexander Hamilton
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What did he do that made him important? 
Alexander Hamilton was in the Continental Army during the American Revolutionary War. At first, in 1775, he joined the New York Militia, but in 1776 he became a Captain in an Artillery Company. He took part in the New York Campaign, at the Battles of Harlem Heights and White Plains. After the Americans were forced to retreat across New Jersey, Hamilton took part in the New Jersey winter campaign in which he fought at the Battles of Trenton and Princeton.
In early 1777, Hamilton was invited to join George Washington's staff. He joined with the rank of Lieutenant Colonel. Hamilton served for four years, in effect, as Washington's Chief of Staff; he handled the "letters to Congress, state governors, and the most powerful generals in the Continental Army"; he drafted many of Washington's orders and letters. Although Hamilton was in a very important position, he wanted to be a commander on the field of battle. Washington thought he was too valuable, and at first refused. However, Washington eventually gave in and Hamilton was given command of a New York light infantry battalion. At the Battle of Yorktown in 1781, he led an assault on Redoubt #10, which compelled the British commander, General Lord Cornwallis, to surrender his entire army.
After Yorktown, Hamilton resigned from the army and was elected to Congress of the Confederation in 1782.