Short answers, pulled from the story.
Rosenborg Castle was originally built in 1606 as a country summerhouse by King Christian IV. The building was expanded several times and reached its present form by 1624. Architects Bertel Lange and Hans van Steenwinckel the Younger were involved in its design.
Rosenborg Castle was commissioned by King Christian IV and designed with architects Bertel Lange and Hans van Steenwinckel the Younger. The castle was built in the Dutch Renaissance style that characterized Danish architecture of the early 17th century.
Rosenborg Castle holds the Crown Jewels and Danish Crown Regalia in a treasury, alongside the Throne Chair of Denmark and a Coronation Carpet. The Long Hall displays the coronation chair of Denmark's absolutist kings and the queens' throne with three silver lions in front. The hall also holds a large collection of silver furniture, most of it from the 17th century.
Rosenborg Castle opened to the public in 1838, when it became state property. It now houses the Royal Collections, spanning from the late 16th century to the 19th century. These include objects from the Danish nobility and aristocracy as well as from royal households.
Rosenborg Castle was last used as a primary royal residence around 1710, after the reign of Frederik IV. It served as a royal refuge only twice afterward: when Christiansborg Palace burned in 1794 and when British forces attacked Copenhagen in 1801. In 1838 the state opened the castle to the public.
The garden surrounding Rosenborg Castle, known as Kongens Have or The King's Garden, attracts an estimated 2.5 million visitors each year. It is the oldest royal garden in Denmark and was embellished by Christian IV before the main castle was built.