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Christianshavn
Facing Indre By and Slotsholmen across the waters of Inderhavnen, and linked to them by Knippelsbro bridge, is the island of Christianshavn . Nicknamed "Little Amsterdam" on account of its many small canals, cobbled streets, crooked houses and brightly painted facades, it's an easygoing area, and a pleasant place to hang out with a  høcker  beer while watching the wooden boats meander up and down the canals.

Until the seventeenth century, however, Christianshavn didn't even exist. The area now occupied by the island was under water, creating a breach in Copenhagen's defences which left the city vulnerable to attack from the sea, until Christian IV reclaimed an arc of land facing Copenhagen and built a ring of defensive fortifications on it. The reclaimed land became the island of Christianshavn and an autonomous borough was created on it to house Dutch merchants, with a Dutch architect - Johan Semp - being employed to plan the new district, explaining the many features on Christianshavn today which are more redolent of Amsterdam than of Copenhagen. The Dutch merchants never arrived, however, and the island was instead distributed between rich Danish merchants and aristocrats, who moved into the elegant dwellings along the waterfront and Wilders Kanal, and the workers, who were assigned the dark and dingy areas between.

Christianshavn's main thoroughfare, Torvegade , runs across the island from mainland Copenhagen in the north towards the island of Amager in the south - at right angles to the picturesque Wilders Kanal that flows down the centre of Christianshavn and divides the island in two. Christianshavns Torv , slap bang in the middle, is the district's busy central square - all buses crossing Christianshavn stop here and it's also the site of a new metro station due to open soon. On the northeastern corner of the island is the so-called "free city" of Christiania , whose improvised dwellings and community of alternative types have long been one of Christianshavn's main tourist attractions. At the far end of Christianshavn are the islands and former naval station of Holmen , now the site of many interesting new cultural developments and well worth exploring on a sunny afternoon.

Indre By
Compared to the monumental edifices of Christiansborg across the Slotsholmen canal, the district of Indre By presents Copenhagen on a more human scale. The heart of both medieval and modern cities, Indre By occupies the site of the Copenhagen area's original settlement, the small and marshy fishing village of Havn, whose fortunes were transformed by the arrival of Bishop Absalon in 1167. Whilst Absalon and his successors raised their castles on the island of Slotsholmen, the settlement of Havn on the mainland opposite prospered through tax and trade, acquiring the name of København ("Merchant's Harbour") and becoming capital of Denmark in 1445.

Within its fortifications - which survive as a ring of parks, lakes and green areas surrounding Indre By - Copenhagen grew rapidly. Although it was ravaged by a series of major fires, as well as being bombarded first by the Swedish, then the British, the medieval town's tangle of tiny streets, squares and ancient churches survived, and is still very much in evidence, in sharp contrast both to the state buildings of Slotsholmen and to the relatively modern areas outside the old fortifications, where permanent settlement only started after 1851.

Nowadays, Indre By (literally, "inner city") is the hub of the city's day-to-day activity and very much the public face of Copenhagen, with lively streets perfectly suited to idle ambling amongst crowds of locals, tourists and street entertainers. Two main pedestrianized thoroughfares cross the area: the first is Strøget , the collective name given to the series of streets (Frederiksberggade, Nygade, Vimmelskaftet, Amagertorv and Østergade) which run across Indre By from Rådhuspladsen in the west to Kongens Nytorv in the east. The second, Købmagergade , leaves Strøget at Højbro Plads, heading north towards Nørreport Station via Kultorvet square. These two main drags form the backbone of the city's shopping district, lined by high-street shops that are all rather mainstream and expensive, though the side streets conceal an intriguing array of second-hand and antique shops, as well as many popular and unusual inner-city bars, cafés and restaurants.  

Norrebo & Osterbro
To the north and east of the Copenhagen's city centre are the districts of Nørrebro  and Østerbro ("North Bridge" and "East Bridge"), built in the mid-nineteenth century on land outside the old city defences. Their similar age apart, the two districts have deeply contrasting histories: Nørrebro's is one of deprivation and social struggle followed by recent immigration and gentrification; Østerbro's is one of traditional wealth and privilege - hence the rather smug feel of the district today, though its leafy ambience makes it a pleasant enough place. 

Rosenborg, Frederikstad and Kastellet
There's quite a contrast between the narrow, tangled streets of Indre By and the open parklands and boulevards of the more modern areas on the northeastern side of the city centre. This part of Copenhagen owes its character to two royal builders, Christian IV - creator of the fanciful palace of Rosenborg Slot  and the more functional fortress of Kastellet  to the north - and Frederik V, whose name is preserved in the district he created, Frederikstad  , a sumptuous royal quarter boasting proud aristocratic monuments such as the Marmorkirken and the palaces of Amalienborg. 

Slotsholmen
The district of Slotsholmen is the historical and geographical heart of Copenhagen. It was here, in 1167, that Bishop Absalon founded the castle that became the nucleus of the future city, and it's been the seat of Danish rule ever since. Here you'll find the highest density of historic sites in Copenhagen, foremost among them the buildings of the massive  Christiansborg complex, comprising all the surviving portions of the various palaces, castles and other royal and governmental edifices which have occupied this site since 1167. At the heart of the complex is the severe grey Christiansborg Slot  , now home to the Danish parliament. Behind Christiansborg Slot, Christiansborg's Outer Courtyard  is all that remains of the original Baroque palace built by Christian VI in the early eighteenth century, while on the northern side of Christiansborg is the recently restored Slotskirke (Palace Chapel) of 1826, and Thorvaldsens Museum, a captivating museum devoted to the work of Denmark's most famous sculptor. South of Christiansborg , the Royal Arsenal Museum, containing the world's largest collection of historical guns and cannons, leads to the Royal Library and its sleek modern extension, the so-called Black Diamond.

Tivoli and Around
Immediately to the west of Indre By, the Tivoli area is Copenhagen's entertainment zone, with virtually every kind of populist amusement you could imagine - if you want to ride one of the world's oldest rollercoasters or inspect a wax model of Hans Christian Andersen, this is the place to come. 

The pleasure gardens of Tivoli themselves are synonymous with Copenhagen at its most innocently pleasurable, while mass-appeal amusements nearby include the mannequin celebrities of Louis Tussauds , the IMAX cinema and astronomical artefacts of the Tycho Brahe Planetarium , and the fun-packed square of Axeltorv . Entertainment of a more aesthetic variety can be enjoyed amongst the statues and assorted flora of the remarkable Ny Carlsberg Glyptotek , one of the jewels in Copenhagen's cultural crown, and the fascinating exhibits of the nearby National Museum .

VESTERBRO AND FREDERIKSBERG 
The two districts immediately west of the city centre, Vesterbro and Frederiksberg, couldn't be more different. Vesterbro has always been determinedly working class, and also has the city's highest multicultural mix - around seventy percent of kids in the local schools are bilingual. Despite encroaching gentrification, it's still one of the most colourful areas of the city, with the broadest selection of affordable ethnic restaurants and shops. 

In stark contrast to Vesterbro's vibrant and colourful street life, Frederiksberg 's wealthy residents tend to stay behind the doors of their grand villas, and the district's spacious and leafy roads are relatively lifeless. Conservative to the core, Frederiksberg is renowned for its low taxes and expensive housing. Situated on the land leading up to Frederiksberg Slot, the king's summer residence, the area was originally used to grow crops and keep livestock to feed the royal household, and was ruled directly by the king. Even now the area retains a regal aura, and is still administered by its own council, independent of the city.