The Oudezijde is the older half, founded in the 13th century, and its spine is the Warmoesstraat, Amsterdam's oldest street. It started life as an address for the wealthy, who moved out to the Canal District in the 17th century once they had built it. Commerce filled the vacuum and never left. The Red Light District runs through the same quarter, along the Oudezijds Achterburgwal, and its trade is older than the wealthy ever were; it dates to the 14th century, when sailors paid for it. The current city government finds the tourist version of it embarrassing and has been trying for years to redirect visitors toward less salacious local attractions. The Nieuwezijde, the newer side, was added in the late Middle Ages and centers on Dam Square, with the Nieuwe Kerk and the looming Royal Palace, a 17th-century city hall that Napoleon's brother Louis converted into a palace and the residents still resent on principle.

Wrapped around the Binnenstad like rings of a tree are the four great canals of the Grachtengordel, built in the 17th century as the world's first deliberately planned urban expansion. The Herengracht, Prinsengracht, Keizersgracht, and Singel were dug in concentric arcs and lined with the tall, narrow merchant houses that gave the city its postcard silhouette. In 2010 UNESCO added the canal ring to its World Heritage list. The reason is not just beauty. Many vistas from Rembrandt's paintings, the wharves of the Geldersekade, the brick gables along the Singel, still look essentially as he painted them. A 17th-century merchant teleported into 2026 would have trouble with the cars and the cyclists, but he would find his way home along the canals without asking directions.

Push east from Dam Square and you reach the Nieuwmarkt, a square dominated by the Waag, a 15th-century city gate turned weighing house turned restaurant. Around it sits Amsterdam's small Chinatown, smaller than the famous ones in San Francisco or London but compact and serious about its food. The Zeedijk, the old sea dike that defined the city's medieval waterfront, now runs through it as a strip of Chinese, Indonesian, and Thai restaurants. The Indonesian presence is colonial inheritance, complicated and delicious; the rijsttafel served in restaurants here was invented by Dutch colonials in 19th-century Java and brought home to the Netherlands as a sort of trophy of the spice trade.

The neighborhood east of the Nieuwmarkt was built outside the medieval walls, and part of it is still called the Jodenbuurt, the Jewish neighborhood. Amsterdam offered an unusual degree of religious freedom from the 16th century onward, and Jewish communities, many fleeing the Iberian Inquisition, settled here in numbers that made the area one of the most distinctive in the city. By the 1920s it was packed with open-air markets and small factories. Then came the German occupation. Most of the Jewish residents of Amsterdam were deported to concentration camps and did not return. The neighborhood went into decay; postwar planners ran a four-lane road through it, and you can still feel the wound. The Joods Historisch Museum, set in a complex of four reclaimed synagogues, holds the memory of who lived here, and the nearby Portuguese Synagogue, built in 1675 and still lit by candles, holds it physically.

The way to see the Binnenstad is to abandon the map. Most of the official sights are clustered around the Damrak and Kalverstraat, and most are not worth the line outside them: the Sex Museum, two competing torture museums, the Hash and Marijuana Museum. The better experience is the city itself. Slip into the side streets that branch off the Spui or thread the Negen Straatjes, the Nine Little Streets, just over in the Canal District. Stop at a brown cafe with stained tobacco walls. Watch the cyclists thread past with the precision of fish in a school. Avoid the bars on Dam Square; they overcharge and underserve. Skip the canal-boat tour for fifteen euros and just walk the canals for free. Amsterdam is one of the few major European capitals where the medieval city is still a living thing rather than a costume, and it rewards the patient visitor in proportion to how slowly they move through it.