A city with a split personality, Amsterdam is both a historic marvel and one of the most youthful metropolises in the world—and you'll get complete servings of both sides of the euro coin in this first, introductory tour.

In fact, a full blast of its two-faced persona will be yours simply by walking into Amsterdam's heart (if not soul): the Dam. For, as the very center of the Centrum, or center city, this gigantic square has hosted many singular sights: Anabaptists running nude in the name of religious freedom, the coronation of kings and queens, stoned hippies camping out under the shadow of its surrealistically phallic National Monument.

The Dam is just one showpiece of the western side of the historic center, known as the Nieuwe Zijde (New Side) and which occupies the district between Damrak (and its extension Rokin) and the Singel canal, just to the west of the sector known as the Oude Zijde (Old Side).

The Dam (Dam Square) remains a useful landmark bridging the older (east) and newer (west) sides of the Centrum. From here you can head off to worship naval heroes in the Nieuwe Kerk or, for some retail therapy, pop into the De Bijenkorf (which lives up to its name—the beehive—during big sales). The core of the oldest part of the city is Amsterdam's most famous area, the Red Light District, known locally as de Wallen, with the aptly named Oude Kerk, its oldest church, bang in the middle. Business in the two main canals and narrow alleyways leading off them is conducted against an implausibly scenic backdrop (porn emporiums and coffee shops at ground level, gables on the top) with atmospheric views from the bridges. (Although this is relative; there's no comparison with the non–Red Light District leafy environs of the southern sections of these same canals below the Damstraat). Its eastern perimeter is Zeedijk, which leads from Centraal Station through Amsterdam's little Chinatown.

There's a bit more in Gelderskade and Nieuwmarkt, where the street opens up into a vibrant square packed with cafés and dominated by the hulking presence of ex–weigh house and medieval gateway, De Waag. Heading southward along the Kloveniersburgwal is a rewarding wander with diversions on both sides of the water: look for churches, chapels, attractive canals, and some notable historic buildings that today house departments of the University of Amsterdam. Farthest west, running parallel to Rokin, is the Nes theater district; heading east is the Old Jewish Quarter, which includes the synagogue complex of the Joods Historisch Museum, Amsterdam's most famous flea market behind the City Hall/Music Theater complex on Waterlooplein, and behind all that, the Rembrandthuis. But if you get lost, even the worst student of foreign languages can easily get help by asking for "Dam Square."