The Dutch were the first to found colonies in the Hudson River Valley, the area comprising most of modern-day New York. They founded the colony of New Amsterdam, which would become New York City, in the early seventeenth century. 

The Vikings, led by the famous Leif Erikson, are believed to have arrived in what is modern-day Nova Scotia and Newfoundland in the eleventh century, four centuries before the arrival of the Dutch, English, French, Portuguese, and Spanish.

The first European colonies in the New World were established in Hispaniola on the initial voyages of Columbus in 1492 and 1493. The island of Hispaniola is now shared by the modern-day countries of Haiti and the Dominican Republic.

The Monroe Doctrine was issued in 1823 following the independence of several South American countries. It stated that if the European powers tried to reestablish colonial control over South or Central America then the United States would intervene. 

Manifest Destiny is an important and influential mythology of the early American Republic. Proponents of Manifest Destiny argued that the United States was fated to spread and expand across the whole North American conflict. Manifest Destiny was an important driving myth in the massive westward expansion of American settlers in the nineteenth century.

The Declaration of Independence, in which the American colonies published a series of grievances against the colonial rule of the British Empire, was written by Thomas Jefferson in 1776. 

The term Revolutionary War is generally used to describe the military campaign between 1775 and 1783, however in terms of a political revolution the period actually began in 1765 when the American colonists first officially rejected the right of the British government to levy taxes against the American colonists. You probably remember the rallying cry "no taxation without representation" from your various classes in American history. This was the central issue that led to the American War of Independence. 

All of these philosophers rose to prominence after the American Revolution, save Hobbes and Locke. Hobbes promoted absolute monarchy, something that the American Revolution fought against. Locke's ideas about a government that responded to the needs of its people influenced the American Revolution.

Napoleon Bonaparte, Emperor of France, invaded Spain in 1807, deposing the King and throwing the country into general chaos. This dissolution of authority made colonial governments assert their own authority over their own lands. By 1833, when King Ferdinand VII of Spain died and the Spanish government renounced claims, only Puerto Rico and Cuba remained as Spanish possessions in the Americas.

The Triple Alliance was the association of Tenochtitlan, Texoco, and Tlacopan, three city states in Central Mexico that came together in the early 1400s CE. This association ruled over much of central Mexico for the next hundred years, with authority vested in the king of Tenochtitlan, although most associated city states had some authority. When Hernan Cortes first encountered and then conquered the Alliance in the early sixteenth century, he and his fellow Spaniards related to it as an "Empire," which they named after the largest ethnic group in the Alliance, the Azteca.