Copenhagen (København) is Scandinavia's most vibrant and affordable capital, and one of Europe's most user-friendly cities. Small and welcoming, it's a place where people rather than cars set the pace, as evidenced by the multitude of pavement cafés and the number of thoroughfares that have been given over to pedestrians and bicycles. Amenable and relaxed, it also offers a range of entertainment which belies its relatively modest size: at night there are plenty of cosy bars and an intimate club and live-music network that could hardly be bettered, while in summer, especially, there's a varied range of entertainment as the city's population takes to the streets. This is not to mention a beckoning range of cultural attractions, including major national museums, a selection of magical art galleries, a healthy assortment of performing arts events and one of Europe's most interesting film scenes.

Physically, much of Copenhagen dates from the seventeenth and eighteenth centuries, a cultured ensemble of handsome renaissance palaces, parks and merchant houses laid out around the waterways and canals that give the city, in places, a pronounced Dutch flavour. Successive Danish monarchs left their mark on the place, in particular Christian IV, creator of many of the city's most striking landmarks - including Rosenborg Slot and the districts of Nyboder and Christianshavn - and Frederik III, who graced the city with the palaces of Amalienborg and the grandiose Marmorkirke church, along with the elegant royal quarter of Frederikstad in which they are located. These landmarks remain the highest points in a refreshingly low and undeveloped skyline which continues to measure things on an emphatically human scale.

Historically, Copenhagen owes its existence to its position on the narrow Øresund strait separating Denmark from Sweden and commanding the entrance to the Baltic - one of the great trading routes of medieval Europe and now the site of the region's grandest engineering project, the massive Øresund Bridge. It's this location, poised on the dividing line between Europe and Scandinavia, that continues to give Copenhagen its distinctive character. Compared to the relatively staid capitals further north, Copenhagen has a decidedly European flavour, from the innocent hedonism of the famous Tivoli gardens to the sleazy goings-on around Vesterbro's red-light district. It's no surprise that the city's most famous export is a beer, Carlsberg, and the freedom with which it flows in the city's thousands of bars is in stark contrast to the puritanical licensing laws found elsewhere in Scandinavia - a fact attested to by the thousands of thirsty Swedes who descend on the city each year. Yet Copenhagen is also a flagship example of the Scandinavian commitment to liberal social values, as exemplified by its laid-back attitudes to everything from gay marriages to toplessness and pornography, and is also home to the unique "Free City" of Christiania, whose drop-out community is one of Europe's most intriguing social experiments.

For all its twentieth-century success, however, the new millennium finds Copenhagen facing an important set of changes and challenges. On the one hand, the magnificent new Øresund Bridge, opened in 2000 to link the city with Malmö and southern Sweden, has given Copenhagen the infrastructure to become the western Baltic's leading urban centre, and there are many who would like to see the city develop into a suitably internationalist and forward-looking metropolis. On the other hand, there are many Copenhageners who regard the bridge, at best, as an irrelevance or, at worst, as a symbol of all those foreign influences that threaten to undermine traditional Danish values. Above all, these influences are typified by Copenhagen's burgeoning immigrant community, and simmering racial tensions - and the resulting rising power of the right wing - pose increasing challenges to the city's tolerant image. At the same time, Denmark's landmark decision in a referendum of October 2000 to opt out of the single European currency also suggests a national desire to remain isolated from the continental mainstream, with the possible result that Copenhagen will be relegated to a position of provincial irrelevance. For all that, it's worth remembering that the city's occasional smugness and resistance to change is the result of its citizens' pride in their capital and determination to protect its unique character, and as a visitor you'll be made to feel welcome wherever you go, especially since absolutely everybody speaks English.

Copenhagen, as any Dane will tell you, is no introduction to Denmark - indeed a greater contrast with the sleepy provincialism of the rest of the country would be hard to find. Thanks to the rapid transport links which connect the capital with its surrounding countryside, however, you can enjoy all the pleasures of rural Zealand without ever being much more than an hour away from the bright lights of the capital. Amongst the many attractions which ring the city are the great castles of Kronborg (the "Elsinore Castle" of Shakespeare's Hamlet ) and Frederiksborg , while the ancient Danish capital and ecclesiastical centre of Roskilde , with its magnificent cathedral and museum of Viking ships, offers another enticing day-trip.

Copenhagen is one of Europe's most manageable capitals: it takes just thirty minutes to walk across the compact centre, and the wealth of green spaces and pedestrianized areas makes exploring the city a relaxed and thoroughly civilized experience. The historic core of the city is the small district of Slotsholmen , originally the site of the twelfth-century castle from which Copenhagen derived its earliest wealth and now home to the city's highest concentration of historic buildings, foremost among them the huge royal and governmental complex of Christiansborg. Facing Slotsholmen over the Slotsholmen Kanal is the medieval maze of Indre By , the bustling heart of the modern city, traversed by Strøget, the world's longest pedestrianized street, and packed with an abundance of swish cafés, shops and bars, and an eclectic clutch of museums and churches. On the opposite side of Slotsholmen from Indre By, the island of Christianshavn - popularly known as "Little Amsterdam" on account of its Dutch-style canals and gabled houses - was built on reclaimed land in the seventeenth century. It's now one of the inner city's most relaxed and bohemian areas, and is also home to the "free city" of Christiania, Copenhagen's famous alternative-lifestyle community.

Northeast of Indre By, the fairy-tale palace of Rosenborg , one of several royal residences in the city, sits at the heart of the inner city's greenest area, with the immaculate lawns of Kongens Have and the lush greenhouses of the Botanisk Have close by. Abutting Kongens Have are the wide, aristocratic streets of Frederikstad , Frederik V's royal quarter, dominated by the huge dome of the Marmorkirke church and centred on the royal palaces of Amalienborg, while just to the north are the green ramparts of Kastellet , Europe's oldest working military fort. Back across Indre By to the south is the city's transport and entertainment hub, grouped around the famous Tivoli pleasure gardens, close to both the city's main transport terminus, Central Station, and its main square, Rådhuspladsen.

Ringing the centre are a series of distinctive and contrasting inner-city areas: to the west, down-at-heel, multicultural Vesterbro , home to the city's red-light district, next to the genteel, villa-lined streets of Frederiksberg , where you'll also find another royal palace, Frederiksberg Slot, and the city's zoo. To the north is the formerly working-class but increasingly gentrified district of Nørrebro , centred on the trendy bars and restaurants of Skt Hans Torv and Blågårdsgade. East of Nørrebro, snooty Østerbro is home to Copenhagen's old money, as well as the national football stadium Parken and the city centre's largest open space, Fælled Park.