When Henry Hudson sailed west from Amsterdam in April 1609, he was looking for a shortcut to the Orient for shipping and trading firm, The Dutch East India Company, which was funding his expedition. Instead, he found what would become New York City and the Hudson Valley. The rest, as they say, is history, and it’s being celebrated in exhibitions and events along the length of the river in this quadricentennial summer.

This is how one of Hudson’s crew described what he saw 400 years ago: “This land is the finest for cultivation that I have ever in my life set upon, and it also abounds in trees of every description. The natives are a very good people, for when they saw that I would not remain, they supposed that I was afraid of their bows, and taking the arrows, they broke them in pieces, and threw them into the fire”—Narratives of New Netherland, 1609-1664.

When Hudson returned to Holland and reported on the bounty of fish, timber and other natural riches, it set off a tidal wave of Dutch immigration: Farmers, fur traders and merchants, some of whom had fled to the liberal Netherlands to escape religious persecution elsewhere in Europe.

Dutch names still define the Hudson Valley.

Harlem is named for Haarlem, a northwestern city and region of the Netherlands. Settlers from Breukelen established a village in what is now Brooklyn. When the Dyckman family left their farm in what is now northern Manhattan to visit their friends, the Bronck family, across the East River, they probably said something like, “see you next week; we are spending the weekend with the Broncks.” A “joncker” is a young nobleman, like the one who founded the village that became Yonkers. Orange County honors the House of Orange, the Dutch royal family; Rensselaer County is named for the Dutch family that settled the area. Kaaterskill Falls is in the southern part of the Catskill Mountains.

Three U.S. presidents had Hudson Valley and Dutch heritage. Martin Van Buren was born in the Dutch settlement of Kinderhook, Columbia County. The Roosevelt family settled in the Hudson Valley in the 1600s; Franklin Delano Roosevelt grew up in Hyde Park, while cousin Theodore lived in New York City and Long Island.

The first senate of New York State met in the little stone house in Kingston built by Abraham van Gaasbeek in 1620, now a state historic site in a historic section of the city called The Stockade, named for the protective wall Peter Stuyvesant ordered built to protect settlers from local natives. That’s also how Wall St. got its name, and many of the streets and alleys in lower Manhattan still have their original Dutch names, including Broadway (Breede Wegh), Coenties Slip and the street named for the most valuable trading product in the 1600s—Beaver Street.

Peter Minuit bought Manna-Hatta island in 1624 from the Lenape Indians for 60 guilders—the equivalent of $24—of beads and iron cooking pots. It was a steal. That same year, Dutch fur traders shipped home 45,000 guilders worth of beaver pelts.

Of course, there’s British history, too. After all, the British captured Nieuw Amsterdam in 1664 and renamed it New York. Ulster County, Westchester County and the city of Albany were named—or re-named—after the Dutch ceded power in 1664. And there very well might be another 400th celebration in 2064. But this year is all about Henry Hudson and the Dutch influence on New York history.

The largest quadricentennial exhibition, at the Museum of the City of New York, includes books on loan from the National Library of the Netherlands. One, a 1656 edition by Adriaen van der Donck, describes the region in detail and contains a map of the entire length of the Mar Nort—not yet renamed the Hudson River. This exhibit is open until September 27. When that closes, another Hudson exhibit of rare maps and documents opens at the South Street Seaport. This is where to go to see the earliest document mentioning that legendary $24 purchase of Manhattan. The so-called Schaghen letter, from 1626, is on loan from Holland’s National Archives.

Hudson and his crew of 20 sailed into history on an 85-foot ship, the Half Moon (“Halve Maen” in Dutch). Hudson first explored the coast of Maine and the Chesapeake and Delaware bays and decided none of these bodies of water were the entrance to the North-West Passage he was seeking. He thought he actually found it in New York Harbor, because much of the Hudson River acts as a tidal estuary, not a river; it’s a body of salt water reaching north until nearly Albany. Only then did he realize it was a river and turned back to claim the newly discovered land for his patrons, the Dutch.

A full-size replica of the Half Moon was built in 1989 in Albany in anticipation of this year’s celebrations, and it’s one of the central players in these quadricentennial events. The sailing ship is on display at the New Netherland Museum in Albany when it isn’t visiting ports as far away as Lake Michigan and North Carolina. This year, it’s doing a lot of visiting, all along the river named for its famous captain. The ship is an accurate replica, so Hudson himself could step aboard and feel right at home, except for the diesel engine and modern GPS navigational aids. But those would no doubt fascinate him.

On July 25 and 26, the Half Moon will be docked at the city of Hudson, the only municipality on the Hudson River named for the navigator. Namesake Weekend is an annual event, but this year it will be very special, with boat tours, fireworks and the dedication of the city’s new waterfront park. In late August, the Half Moon will set sail for a weekend of public tours alongside Staten Island; in early September, she is the star of the annual Peekskill Celebration at Charles Point Park, and then she’ll take part in the NYC Harbor Day weekend before going on to Albany. Each year on the anniversary of Henry Hudson’s arrival in the state capital on September 19, the people of Albany  celebrate with two weeks of tours and exhibits at the Hudson River Waterfront. As important as the Half Moon is to the quadricentennial celebration, it’s not the only historic ship involved. A flotilla of distinctive flat-bottom Dutch fishing boats and barges will be sailing up and down the Hudson River for two weeks in September, taking part in sailing races and offering tours. These boats are the direct descendents of the sailing ships that served the Dutch coastline in the 17th and 18th centuries, and the first ships built in New Amsterdam.

Another museum exhibit looks at Dutch influence and culture in the Hudson Valley at specific times: The Half Moon’s arrival in 1609; under English rule circa 1709; Washington Irving’s stories of Dutch heritage in 1809; celebrations of a common Dutch past in 1909, and a debate over what all these historical celebrations mean to us in 2009. It’s at the Hudson River Museum in Yonkers through Jan. 10.

What happened to Henry Hudson after he claimed his namesake New York region? Nobody knows for sure. On his next journey, in 1611, to what is now the Hudson Bay in Canada, his crew mutinied. They wanted to go home; he wanted to continue exploring. Hudson, it is thought, was set adrift in a lifeboat along with his son and eight loyal crewmen.