After the U.S. Constitution was ratified, Congress passed the "Mint Act" of April 2, 1792, which established the coinage system of the United States and the dollar as the principal unit of currency. By this Act the U.S., became the first country in the world to adopt the decimal system for currency. The first U.S. coins were struck in 1793 at the Philadelphia Mint and presented to Martha Washington.
The government did not issue paper money until 1861. In the interim years, however, the government did issue "Treasury notes" intermittently during periods of financial stress, such as the War of 1812, the Mexican War of 1846, and the Panic of 1857.
During this same period (1793 - 1861), approximately 1,600 private banks were permitted to print and circulate their own paper currency under state charters. Eventually, 7,000 varieties of these "state bank notes" were put in circulation, each carrying a different design!
With the onset of the Civil War, the government - desperate for money to finance the war - passed the Act of July 17, 1861, permitting the Treasury Department to print and circulate paper money. The first paper money issued by the government were "demand notes" commonly referred to as "greenbacks." In 1862, Congress retired the demand notes and began issuing United States notes, also called legal tender notes.