New York City, the most populous city in the United States, is known for its status as a financial, cultural, transportation, and manufacturing center, and for its history as a gateway for immigration to the United States. According to the U.S. Department of Commerce, it is also a destination of choice for many foreign visitors. Both state and city were named for the 17th century Duke of York, James Stuart, future James II and VII of England and Scotland.

New York was inhabited by the Algonquin, Iroquois, and Lenape Native American groups at the time Dutch settlers moved into the region in the early 17th century. In 1609, the region was first claimed by Henry Hudson for the Dutch. Fort Nassau was built near the site of the present-day capital of Albany in 1614. The Dutch soon also settled New Amsterdam and parts of the Hudson River Valley, establishing the colony of New Netherland. The British took over the colony by annexation in 1664.

The borders of the British colony, the Province of New York, were roughly similar to those of the present-day state. About one third of all the battles of the Revolutionary War took place in New York. New York became an independent state on July 9, 1776, and enacted its constitution in 1777. The state ratified the United States Constitution on July 26, 1788 to become the eleventh state of the union.

New York covers 54,556 square miles (141,300 km2) and ranks as the 27th largest state by size. The Great Appalachian Valley dominates eastern New York, while Lake Champlain is the chief northern feature of the valley, which also includes the Hudson River flowing southward to the Atlantic Ocean. The rugged Adirondack Mountains, with vast tracts of wilderness, lie west of the valley.

Most of the southern part of the state is on the Allegheny Plateau, which rises from the southeast to the Catskill Mountains. The western section of the state is drained by the Allegheny River and rivers of the Susquehanna and Delaware systems. The Delaware River Basin Compact, signed in 1961 by New York, New Jersey, Pennsylvania, Delaware, and the federal government, regulates the utilization of water of the Delaware system. The highest elevation in New York is Mount Marcy in the Adirondacks.

New York's borders touch (clockwise from the west) two Great Lakes (Erie and Ontario, which are connected by the Niagara River); the provinces of Ontario and Quebec in Canada; Lake Champlain; three New England states (Vermont, Massachusetts, and Connecticut); the Atlantic Ocean, and two Mid-Atlantic States, New Jersey and Pennsylvania. In addition, Rhode Island shares a water border with New York. New York is the only state that touches both the Great Lakes and the Atlantic Ocean.

In contrast with New York City's urban atmosphere, the vast majority of the state is dominated by farms, forests, rivers, mountains, and lakes. New York's Adirondack Park is the largest state park in the United States. It is larger than the Yellowstone, Yosemite, Grand Canyon, Glacier and Olympic National Parks combined. New York established the first state park in the United States at Niagara Falls in 1885. Niagara Falls, on the Niagara River as it flows from Lake Erie to Lake Ontario, is a popular attraction.

The Hudson River begins at Lake Tear of the Clouds and flows south through the eastern part of the state without draining Lakes George or Champlain. Lake George empties at its north end into Lake Champlain, whose northern end extends into Canada, where it drains into the Richelieu and then the St. Lawrence Rivers. Four of New York City's five boroughs are on three islands at the mouth of the Hudson River: Manhattan Island; Staten Island; and Long Island, which contains Brooklyn and Queens on its western end.

Upstate and downstate are often used informally to distinguish New York City or its greater metropolitan area from the rest of New York state. The placement of a boundary between the two is a matter of great contention. Unofficial and loosely defined regions of Upstate New York include the Southern Tier, which often includes the counties along the border with Pennsylvania, and the North Country, which can mean anything from the strip along the Canadian border to everything north of the Mohawk River.

In general, New York has a humid continental climate, though under the Köppen climate classification, New York City has a humid subtropical climate. Weather in New York is heavily influenced by two continental air masses: a warm, humid one from the southwest and a cold, dry one from the northwest.