AMSTERDAM is a beguiling capital, a compact mix of the provincial and the cosmopolitan. It has a welcoming attitude towards visitors and a uniquely youthful orientation. For many, however, its world-class museums and galleries - notably the Rijksmuseum, with its collection of seventeenth-century Dutch paintings, and the Van Gogh Museum - are reason enough to visit.

Amsterdam was founded on a dam on the river Amstel in the thirteenth century. During the Reformation it rose in stature, taking trade away from Antwerp and becoming a haven for its religious refugees. Having shaken off the yoke of the Spanish, the city went from strength to strength in the seventeenth century, becoming the centre of a vast trading empire with colonies in Southeast Asia. Amsterdam accommodated its expansion with the cobweb of canals that gives the city its distinctive and elegant shape today. Come the eighteenth century, Amsterdam went into gentle decline, re-emerging as a fashionable focus for the alternative movements of the 1960s. Despite a backlash in the 1980s, the city still takes a uniquely progressive approach to social issues and culture, with a buzz of open-air summer events, intimate clubs and bars, and relaxed attitude to soft drugs.

Amsterdam is a small city, and, although the concentric canal system can be initially confusing, finding your bearings is straightforward. The medieval core boasts the best of the city's bustling streetlife and is home to shops, many bars and restaurants, fanning south from the nineteenth-century Centraal Station , one of Amsterdam's most resonant landmarks and a focal point for urban life. Come summer there's no livelier part of the city, as street performers compete for attention with the trams that converge dangerously from all sides. From here, Damrak storms into the heart of the city, an unenticing avenue lined with overpriced restaurants and bobbing canal boats, and flanked on the left first by the Beurs , designed at the turn of the twentieth century by the leading light of the Dutch modern movement, H.P. Berlage, and then by the enormous De Bijenkorf department store.

To the left off Damrak, the infamous red-light district , stretching across two canals - Oudezijds (abbreviated to O.Z.) Voorburgwal and O.Z. Achterburgwal - is one of the real sights of the city, thronged in high season with visitors keen to discover just how shocking it all is. Though seamy and seedy, the legalized prostitution on flagrant display here is world-renowned. The two canals, with their narrow connecting passages, are thronged with neon-lit "window brothels", and at busy times the crass on-street haggling over the price of various sex acts is drowned out by a surprisingly festive atmosphere.

Just behind the Beurs off Warmoesstraat, the precincts of the Oude Kerk (Mon-Sat 11am-5pm, Sun 1-5pm; ?3.60; www.oudekerk.nl ) offer a reverential peace after the excesses of the red-light district; it's a bare, mostly fourteenth-century church with some beautifully carved misericords in the choir and the memorial tablet of Rembrandt's first wife, Saskia van Uylenburg. Nearby, the Amstelkring , at the northern end of Oudezijds Voorburgwal, was once the principal Catholic place of worship in the city and is now a museum (Mon-Sat 10am-5pm, Sun 1-5pm; ?4.50) commemorating the days when Catholics had to confine their worship to the privacy of their homes. Known as "Our Dear Lord in the Attic", it occupies the loft of a wealthy merchant's house, together with those of two smaller houses behind it. Just beyond, Zeedijk , once haunt of Amsterdam's drug dealers, leads through to the open Nieuwmarkt , where the turreted Waag was originally part of the city's fortifications, later becoming the civic weigh-house. Kloveniersburgwal , which leads south, was the outer of the three eastern canals of sixteenth-century Amsterdam and boasts, on the left, one of the city's most impressive canal houses, built for the Trip family in 1662. Further up on the right, the Oudemanhuispoort passage, once part of an almshouse, is now filled with secondhand bookstalls.

At the southern end of Damrak, the Dam (or Dam Square), where the Amstel was first dammed, is the centre of the city, its tusk-like War Memorial serving as a meeting place for tourists. On the western side, the Royal Palace (June-Oct daily 11am-5pm; Nov-May opening hours variable; ?4.30; www.kon-paleisamsterdam.nl ) was originally built as the city hall in the mid-seventeenth century. It received its royal monicker in 1808 when Napoleon's brother Louis commandeered it as the one building fit for a king. He was forced to abdicate in 1810, leaving behind a sizeable amount of the Empire furniture. Vying for importance is the adjacent Nieuwe Kerk (open only during exhibitions; www.nieuwekerk.nl ), a fifteenth-century structure rebuilt several times, which is now used only for exhibitions and state occasions. Inside rest numerous names from Dutch history, among them the seventeenth-century naval hero Admiral de Ruyter, who lies in an opulent tomb in the choir, and the poet Vondel, commemorated by a small urn near the entrance.

South of Dam Square, Rokin follows the old course of the Amstel River, lined with grandiose nineteenth-century mansions. Running parallel, Kalverstraat is a monotonous strip of clothes shops, halfway down which, at no. 92, a gateway forms the entrance to the former orphanage that's now the Amsterdam Historical Museum (Mon-Fri 10am-5pm, Sat & Sun 1-5pm; ?6.10; www.ahm.nl ), where artefacts, paintings and documents survey the city's development from the thirteenth century. Directly outside, the glassed-in Civic Guard Gallery draws passers-by with free glimpses of the large company portraits. Just around the corner, off Sint Luciensteeg, the Begijnhof is a small court of seventeenth-century buildings; the poor and elderly led a religious life here, celebrating Mass in their own, concealed, Catholic Church. The plain and unadorned English Reformed Church, which takes up one side of the Begijnhof, has pulpit panels designed by the young Piet Mondriaan. Close by, the Spui (pronounced spow ) is a lively corner of town whose mixture of bookshops and packed bars centres around a cloying statue of a young boy known as 't Lieverdje (Little Darling). In the opposite direction, Kalverstraat comes to an end at Muntplein and the Munttoren - originally a mint and part of the city walls, topped with a spire by Hendrik de Keyser in 1620. Across the Singel canal is the fragrant daily Flower Market , while in the other direction Reguliersbreestraat turns left towards the loud restaurants of Rembrandtplein . To the south is Reguliersgracht, an appealing canal with seven distinctive steep bridges stretching in a perspectival line from Thorbeckeplein.