This is the royal residence. 

The palace was built in the mid 1700's for four very rich noblemen, which is why it has four almost identical palaces. Amalienborg became the royal residence after Christiansborg Palace - not too far away - burned down in 1794.

When members of the royal family are at home the flag is hoisted upon the palace where they live. In the palace to the right towards the waterfront, the Crown prince- and princess live with their four children, and in the palace to the left towards the waterfront, the Queen lives. There is a joke that the Queens palace has an extra chimney because she smokes, but that’s of course not true. 

You can visit Christian the 8th’s palace which is part of the Amalienborg Museum. 

The Amalienborg Museum reaches 150 years back in time to Christian the 9th and Queen Louise, who became known as "Europe's in-laws" because four of their children ascended the thrones of Europe as Empress of Russia, Queen of England, King of Greece and King of Denmark, respectively.

Entrance is €16 (€10 for students) and free with the Copenhagen Card