Finished in 1642, the Round Tower was constructed to serve as an astronomical observatory. The path to the top of the tower uses a sloped ramp in place of stairs, making for a highly unusual climb and fun experience.
The top of the tower has a large viewing platform on it which allows scenic views of central Copenhagen.
While not regularly available and subject to Denmark's turbulent weather, each winter when the nights are long and the skies clear, they open the observatory to the public for limited evening viewings. As you can imagine, due to Copenhagen's near-constant daylight in the summer, this isn't available year-round.