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A walking tour of central Copenhagen. 15 stops, 6.1 km, around two hours at an easy pace. The walk runs from City Hall Square to The Little Mermaid and covers the old town, Slotsholmen, the harbour front and Frederiksstaden. There is no fixed order: you can join anywhere, skip stops and turn back, and each point plays when you enter its geofence.

Notice how much space there is around you. In Copenhagen that is unusual, and there is a reason for it. Until the middle of the nineteenth century the city was squeezed in behind its ramparts, and building in stone outside the walls was forbidden, in case an enemy should use the houses for cover. People lived on top of each other in streets you can still walk down, some of them barely two metres wide. When the ramparts came down from 1856, it was like opening a window in a room that had been shut for three hundred years. This square is the first breath the city took. The City Hall was inaugurated in 1905. Look up at the balcony and you will find Bishop Absalon in gold, the man who founded the city. But the best story is inside. A locksmith named Jens Olsen spent much of his life calculating an astronomical clock. He never saw it run. He died in 1945, ten years before it was finished, and it was King Frederik IX who set it going in December 1955. The clock is still running. Its slowest gear takes 25,753 years to complete one single revolution, so the last time it sat where it sits now, northern Europe was under ice.

Behind this facade lies the oldest history in Denmark, and two of the objects inside are worth knowing about even if you do not go in. The first is the Sun Chariot. A bronze horse pulling a large disc on wheels, found in a bog in 1902 and made around 1400 BC. What matters is that the disc is gilded on one side only. The people who made it believed the sun is drawn across the sky from east to west by day, showing us its gold side, then travels back through the night with the dark side turned to the earth. That is a complete explanation of why it gets dark, worked out by people with no written language. The second is the Egtved Girl. She was buried in a hollowed oak log three and a half thousand years ago, and because the coffin filled with water she is preserved as almost nothing else is. Her hair, short and blonde. Her nails, neatly trimmed. Her string skirt and woollen belt. In a small box of birch bark lay an awl, some bronze pins and a hairnet. Then come the details that make her a person. At her feet lay the burned remains of a child of five or six. On her body someone had placed flowering yarrow, which blooms only in summer, so we know the season she was buried in. Beside her stood a bucket of beer, brewed from wheat, honey, bog myrtle and cowberries. She was sixteen or seventeen years old.

You are standing between two squares that look like one, and that is not an accident. Gammeltorv has been the city's marketplace since the twelfth century. Nytorv was cleared around 1610. When the town hall between them burned in 1795, the whole area was rebuilt into the long room you see now. Look down. Somewhere under your feet the cobbles change colour in a rectangle of paler stone. That is the outline of the town hall that burned. The city chose to mark where it stood rather than forget it, which is fairly typical of Copenhagen. The fountain is the Caritas Well, put up by Christian IV in 1608. The figure is a pregnant woman with two children, and the water runs quite literally from her breasts. Caritas means charity. On the monarch's birthday, gilded copper balls are placed in the basin and dance on top of the water jets like golden apples. And then the thing that makes this square strange. Nytorv, the half either in front of you or behind you, was the city's place of execution. Sentences were read out here and carried out here, with a crowd around. So for centuries the city's image of charity and the place where people were put to death stood within sight of one another. Nobody saw a contradiction in it.

This church looks bare and severe compared to most of the city, and the reason is brutal. In early September 1807 a British fleet lay off Copenhagen. Denmark was neutral but had a navy, and the British would not risk Napoleon getting the use of it. When the city refused to hand it over, the bombardment began. It went on for three nights. The British fired around three hundred Congreve rockets into the houses, among the first incendiary rockets used against a city, and more than a thousand buildings burned. Close to two hundred civilians were killed. The cathedral standing here then had the tallest spire in town. British gunners used it as a ranging mark to sight their guns, and set it alight in the process. The tower came down and the church burned to the ground. The one you see now was designed by C.F. Hansen and finished in 1829. He chose a severe neoclassical style with almost no ornament. If you go inside, Bertel Thorvaldsen's figure of Christ stands above the altar. Look at the arms. They are not raised in blessing as you would expect, but lowered and open. You have to walk right up and look up underneath them to meet the face. That was shaped on purpose. You have to come closer. The square around you belongs to the university, founded in 1479.

Christian IV had a weakness for building, and this may be the strangest thing he put up. The tower was finished in 1642 as an observatory, and it is still the oldest working one in Europe. Go inside and you will see what makes it odd. There is no staircase. Instead a cobbled ramp winds in a spiral all the way to the top, a little over two hundred metres long and wide enough for a horse and cart. This was not royal whimsy. The astronomers needed heavy, fragile brass instruments at the top, and nobody wanted to carry them up stairs. Which led to the scene the tower is best known for. In October 1716 Tsar Peter the Great was visiting Copenhagen. He rode up the ramp on horseback, the whole way, inside the tower. Tsarina Catherine refused to ride, but would not walk either, so she was driven up behind him in a four-wheeled carriage pulled by six horses. The head of the observatory, an astronomer called Peder Horrebow, stood and watched the whole thing. He wrote it down, and the city paper printed it. That is how we know it actually happened and is not just a good story. If you make it to the top, you can see the whole old city at once.

The man on the horse above you is Bishop Absalon, and notice how he is shown. He sits in full armour on a rearing horse, and what he holds in his hand is a battle axe. That is not the usual way to depict a bishop. But Absalon was no usual bishop. He was the king's closest man, a commander and a politician, and in 1167 he built the castle that became Copenhagen. He points that axe straight across the canal, at the islet where the castle stood. The statue dates from 1901, seven hundred years after his death, and the plinth beneath him was designed by Martin Nyrop, the same man who designed Copenhagen City Hall. Where you stand is the line between two Copenhagens. Behind you is Strøget and the merchant town, where the money was made. In front of you, across the bridge, is Slotsholmen, where it was spent. And one last thing that almost everyone walks straight past. Go to the edge of the bridge and look down into the water. Below the surface lies a bronze mermaid. She has no sign, no queue and no tour buses, and she is visible only when the water is still enough. She is not the famous mermaid out at Langelinie. She is another one, lying down here waiting for somebody to look.

This is where the city began. In 1167 Absalon built a castle of limestone and flint out here on the islet, not to live grandly but to keep pirates out of the sound. A village grew around it, the village became a harbour, and the harbour became a capital. The castle is gone. But go down into the cellars beneath the palace and you are standing inside it. The ruins of Absalon's curtain wall and foundations were excavated and opened to the public in 1924, and you can put your hand on masonry he had built. It is the oldest thing in Copenhagen you are allowed to touch. Above it, this plot has had trouble holding on to a building. The first Christiansborg burned in 1794 and left the royal family homeless. The second burned in 1884. The third, the one in front of you, went up between 1907 and 1928 and has been allowed to stand so far. And there is something about this house that exists nowhere else in the world. Parliament sits here and makes the laws. The Supreme Court sits here and rules on them. The royal family keeps its state rooms in the same building. Three branches of government, one address, one roof. In most countries somebody would have called that a bad idea. The tower is open to visitors, and the view from it is the best in the city.

For almost four hundred years this house was the easiest way to draw Copenhagen. Christian IV had it built in the 1620s as a centre of trade, in red brick with Dutch gables, and on top he put a spire like nothing else: four dragon tails braided together and twisted up towards the sky. On the morning of the sixteenth of April 2024 the building caught fire. It was under restoration, and the flames took hold in the loft where the scaffolding and tarpaulins were. It spread faster than anyone could stop it. What happened in the hours that followed is why the date means something to Danes. While it burned, people ran into the building to save the art. Staff, firefighters, and passers-by who simply happened to be walking there. They carried out painting after painting. The largest was several metres across and came out of the smoke in the arms of people who had never met. The pictures from that morning went around the world. After a few hours the dragon spire buckled and fell. Around half the building was lost. What you are looking at is a house in the middle of being raised again. The rebuilding uses more than 800,000 handmade bricks, made by old methods, and is planned to be finished in 2029. The spire is coming back.

In 1669 Christian V was crowned, and he had spent time in France. He had seen Paris, and he came home to a city that still looked medieval: narrow streets, no plan, nothing that impressed anyone. So he cleared this ground. It sat just outside the old city gate and consisted mostly of ramparts, rubbish and an old ropewalk. In 1670 he laid out Copenhagen's first planned square here, on the French model, with himself in an equestrian statue in the middle. Look closely at that statue. The king is dressed as a Roman emperor, in a laurel-wreathed helmet. It dates from 1688 and is the oldest equestrian statue in Scandinavia. The original was cast in gilded lead, and that went about as well as you would expect: over two hundred years the king slowly sagged under his own weight, until he finally had to be recast in bronze. It is hard to find a better image of absolute monarchy than a king of lead, sinking. Around the square stand the Royal Danish Theatre, Charlottenborg with the art academy, and the Hotel d'Angleterre. And notice one thing. Every building here turns its front towards the square. That was the whole point. This was not meant to be a place you walked through. It was meant to be a place you arrived at.

This canal was dug out by hand, and it is worth knowing who did it. Christian V started the work in 1670. The men standing in the mud digging were Danish soldiers and Swedish prisoners of war, taken in a war the king had just lost. It took five years. The idea was to let ships sail right up to Kongens Nytorv so cargo could be unloaded in the middle of town. It worked. And the result was not the colours you see now. For two hundred years this was the harbour quarter, with everything that comes with one: taverns, tattoo parlours, brothels and sailors coming ashore with wages in their pockets. Respectable people did not come here. They did not send their daughters here. And in the middle of all that lived Hans Christian Andersen. He kept rooms at number 67 from 1845 to 1864, and later at number 18 until he died in 1875. Eighteen years in all, in the part of town with the worst reputation. The man who wrote the fairy tales children grow up with all over the world wrote them looking out at a harbour full of drunk sailors. The ships went after the war, the canal sat half empty, and it was only from the 1960s that the cafés and the colours arrived. The houses on the sunny side date from the late seventeenth century. The oldest of them are as old as the canal.

Four identical mansions around an octagonal square, with Frederik V on horseback in the middle. It looks like something built for a royal family. It was not. Nicolai Eigtved laid it out in the 1750s as the heart of an entirely new district, Frederiksstaden, and the four mansions went up for four noble families who could afford them. The king lived where kings lived, at Christiansborg. Then Christiansborg burned in 1794. The royal family suddenly had nowhere to live, in the middle of a Danish winter, and the solution was the simplest one available: they bought the mansions from the nobility. They moved in that December, and they have never moved out. What was meant to be temporary has lasted more than two hundred years. Turn around where you stand. The axis through Frederiksgade is set so that it meets the dome of the Marble Church at one end. Turn the other way and the line carries on across the harbour and hits the Opera House. That part was not planned in the 1750s, because the Opera only arrived in 2005, but they placed it exactly on the sightline. The Royal Life Guards march out from Rosenborg at half past eleven and change the guard here at noon. If the monarch is at home the flag flies over the palace, and the changing comes with a full band.

The dome above you is the largest in Scandinavia, thirty-one metres across. It is also the end point of the most embarrassing building project in Danish history. Frederik V laid the foundation stone on the thirty-first of October 1749. The architect Nicolai Eigtved had drawn a church in Norwegian marble, on a scale meant to stand comparison with St Peter's in Rome. That was how the king wanted Denmark to look. Then Eigtved died. The marble from Norway turned out to cost far more than anyone had reckoned with. And in 1770 Struensee cut the funding entirely. Work stopped. And there it stood. Not for a few years, but for almost a hundred and fifty. A half-finished, open ruin in the middle of the city's finest new district, right beside where the royal family would soon be living. People took stone from it for their own houses. Painters came to sketch it, because in the nineteenth century a ruin was the most romantic subject there was. For a few generations the church was far more famous as a ruin than it ever became as a church. It took a businessman to sort it out. C.F. Tietgen bought the site in 1874 and paid to have it finished, now in Danish limestone instead of marble. The church was consecrated on the nineteenth of August 1894, a hundred and forty-five years after the foundation stone was laid.

You are walking around inside a working fortress. Kastellet is shaped as a five-pointed star with a bastion at each corner, and it is one of the best preserved works of its kind in northern Europe. It is still a military area. It is also a public park. Those two things have existed side by side here for over three hundred years. It got its shape after the Swedes laid siege to Copenhagen from 1658 to 1660. The city held through a winter that should have broken it, and afterwards the king decided the northern flank would never lie open again. The gates date from 1663. The King's Gate, the one facing the city, carries garlands, pilasters and a bust of Frederik III. The windmill up on the King's Bastion is from 1847 and is the last of sixteen rampart mills that once ground grain around the whole city. It still works. But look closely at the church from 1703, and at the wall behind it. The prison stood there. And set into the wall between the prison and the church are small sound holes. They were made on purpose, so that prisoners could hear the service without being let into the church. They were given the words but not the room. There are few places where an entire era's view of punishment and salvation is built so plainly into a wall.

This fountain tells a story, and it is worth hearing the whole of it. The Norse goddess Gefion came to Gylfi, the king of Sweden, and he made her a promise he probably thought was both generous and safe: she could have all the land she managed to plough in a single day and night. Gefion went to the land of the giants. There she had four sons by a giant, and the sons of a giant are not ordinary boys. She turned them into oxen, yoked them to the plough and set to work. They pulled so hard and cut so deep that the plough did not merely turn the soil. The whole piece of land tore loose from the ground. She dragged it out to sea and let it go. That piece of land is Zealand, the island you are standing on. The hole left behind in Sweden filled with water and became Lake Vänern, and if you lay the two maps beside each other, they fit together rather well. Anders Bundgaard carved the figures between 1897 and 1899. The water was turned on in July 1908. It was a gift to the city from the Carlsberg Foundation, marking the brewery's fiftieth anniversary. The red brick church beside it is St Alban's, the English church in Copenhagen, consecrated in 1887.

First the important thing: she is 1.25 metres tall. That is worth saying straight away, because it is what surprises people most, and the disappointment goes away once somebody says it first. The story begins in 1909, at the Royal Danish Theatre. Carl Jacobsen, the brewer behind Carlsberg, sat in the audience watching a ballet of Hans Christian Andersen's fairy tale. He was so taken with what he saw that he walked out and commissioned a statue, and the work went to the sculptor Edvard Eriksen. Eriksen knew who he wanted as his model: Ellen Price, the ballerina who had danced the part. She agreed to meet him, and refused to pose nude. So Eriksen asked his own wife, Eline, and it is her you are looking at. The whole figure is Eline Eriksen. The widespread story that the head is Ellen Price has followed the statue for over a century, and it is not true. She was unveiled on the twenty-third of August 1913, and she has had a rough life since. Her head has been sawn off and stolen twice, in 1964 and in 1998. Her right arm went missing in 1984. In 2003 she was blasted off her base. Through all of it she has been repaired and put back on the same stone, every single time.