Google what you think and the answer will be (as Arthur Askey used to say, "Before your very eyes!"
You fellas (and lasses) just amaze me with your knowledge!
The Round Tower was built by Christian IV between 1637 and 1642. It was the first part of the Trinitatis Complex, which combined church, library and observatory in a single building.
The Tower once soared far above the rest of the rooftops in the city, and University astronomers studied the stars and planets from the Observatory at the top. The scholars may have forsaken the building a long time ago, but during the winter visitors are still able to gaze at the cosmos from Europe's oldest functioning observatory. The platform that runs around the outside of the Observatory affords views over the old Latin Quarter – from here, you can spot most of the city's famous buildings.
5 points for that Fester. Lovely city to visit. I did Copenhagen when I worked for the Swedes