Three days in Trondheim: Norway's first capital, now mostly run by students

Go to the cathedral first. It is the largest medieval building in Norway and the only Gothic cathedral in the country, begun in the eleventh century over St Olav's grave and worked on for two hundred years, then burnt, wrecked, partly demolished and finally rebuilt over a restoration that ran from 1869 to 1969. The west front is a wall of statues, most of them twentieth century replacements carved to medieval designs, and one of the sculptors put Bob Dylan's face on a minor figure, which the cathedral has decided not to mind about. The octagonal chapel at the east end was built to hold the shrine; the shrine itself was taken to Denmark and melted down at the Reformation, and the grave has never been found since. Climb the tower if it is open.

The archbishop's palace next door holds the crown jewels of Norway in a vault, and an excavation museum under the courtyard with the mint where medieval coins were struck.

In the afternoon walk down to the river. The Old Town Bridge dates in its present form from 1861, is painted red, and has arched portals at each end that Trondheim calls the gate of happiness. From it you look down at the row of wooden warehouses standing on piles in the water, which is the photograph of the city. Cross into Bakklandet, a district of small painted timber houses that was condemned for a motorway in the 1970s and saved by the people living in it. It is now cafés, second hand shops and the best afternoon in Trondheim.

Sverresborg is a twenty minute bus ride west and is the open air museum of the Trøndelag region: eighty or so buildings moved here from farms, villages and the town, including a small stave church from Haltdalen built around 1170, which is one of the oldest wooden buildings in Norway and considerably plainer than the famous ones. The site is named after King Sverre, who put a castle on this rock in the 1180s, and the ruins are still up there. In summer there are people working the buildings in period clothes and animals in the farmyard.

In the afternoon take the boat out to Munkholmen. The island a kilometre and a half offshore was an execution ground before it was anything else, then a Benedictine monastery from the eleventh century, then a fortress, then a prison holding political prisoners for two hundred years, then a German gun position, and now it is where Trondheim goes swimming. The ferry leaves from Ravnkloa in the middle of town, takes about ten minutes and only runs in the summer season. There is a café and a small beach.

Finish at Kristiansten, the fortress on the ridge east of the river, built in the 1680s after the great fire to stop the Swedes taking the town from above. It worked: a Swedish army under Armfeldt turned back from here in 1718 and then lost thousands of men to a blizzard retreating over the mountains. The Germans used the courtyard for executions during the occupation and there is a memorial. The view over the whole city and out to the fjord is the best in Trondheim and the walk up is fifteen minutes.

Rockheim is on the quay just behind the station, in a converted grain warehouse with a glass box cantilevered out over the top of it, and it is the national museum of Norwegian popular music. That sounds parochial and mostly is not: it runs from the 1950s upwards, floor by floor, it is heavily interactive, and you can mix a track, play a drum kit badly and stand inside a black metal exhibit that takes its subject entirely seriously. Give it ninety minutes.

Then walk five minutes to Stiftsgården on the main street, which is the largest wooden building in Scandinavia: a hundred and forty rooms behind a plain yellow front, built in the 1770s by a wealthy widow determined to outdo her neighbours, and now the royal family's Trondheim residence. It is open for guided tours in summer when nobody is staying, and the tour is the way to see the interiors.

The station is ten minutes' walk, and the airport train leaves from the same platforms.