The oldest buildings date back to medieval times.
The Church of the Holy Ghost 
Halfway down Strøget, the main pedestrian shopping street, you will find The Church of the Holy Ghost. Next door is a building dating from the days of Christian I (1448-1481). It was originally a monastery hospital. Today it is used for exhibitions and occasional concerts.
Jarmer's Tower,
or what is left of it, was built in the 1200's. It is named after a Wendish chieftain called Jaromar who broke through the fortified town wall at this spot in a siege in one of the many wars between the Church and the Monarchy in the 1200's. You will find it where Nørrevoldgade meets Vester Voldgade.
Copenhagen University
In the courtyard of the University you will find the remains of an old bishop's palace from app. 1420. In the cellar supported by granite columns insubordinate students were placed as punishment for disorderliness.
Underneath Christiansborg Palace remains of the original fortress built by Bishop Absalon in 1167 can still be seen.