Christian IV started Rosenborg in 1606 as a summerhouse at the edge of Copenhagen, and kept extending it until it was finished in 1624. It is Dutch Renaissance — red brick, sandstone dressings, copper spires — and it was never a fortress or a seat of government. It was where a king went to be comfortable, which is why it still feels like a house rather than a state building.
The Treasury is in the basement and it is the reason most people come. The Danish Crown Regalia are kept here, along with the Crown Jewels, and unlike most European regalia they are still the working property of the monarchy rather than museum pieces. Upstairs, the Long Hall was finished in 1624 and holds the coronation chair of the absolutist kings, the queens' throne, and the three silver lions that stand in front of them.
The castle opened to the public in 1838, which makes it one of the older museums in Europe, and the collection runs from the late 1500s through the 1800s. Twelve tapestries in the Long Hall record Christian V's victories in the Scanian War. Allow ninety minutes or so — the rooms are small, the staircases are narrow, and it is not a building you can rush.