The royal residence in Copenhagen consists of 4 different mansions around a square. The queen has two of these mansions at her disposal and the crown prince has one. The last of the mansions has partly been made into a museum about the royal family.
You can go and visit the museum if you want to learn a bit more about the royal family which is now living at the other mansions. The museum is displaying some of the rooms which the former kings lived in with the original furnishing and the different items they had inside their studies.
The rooms seems a bit more clothed than what I would have thought the royal family lived – I guess they were a bit of collectors of stuff – so even with the many rooms they still filled out them all.
You can wonder around the rooms and see how the old kings lived and there is a bit of information available in Danish and English so you can learn more about the royal family of Denmark which is the oldest of the ruling royal families in Europe. The current queen is a descendent of King Gorm the old who ruled around the middle of the 9th century and were the first king of a united Denmark.
If you like you can make the visit to the museum part of a royal day where you start by visiting the Rosenborg Castle in the morning and then head for Amalienborg in time to see the changing of the guard at noon and visit the museum either before or after the changing of the guard. There is a discount ticket which will give you access to both the Rosenborg castle which is a very pretty little castle and the Amalienborg museum.