In the Schlossgarten park.
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Built to supply the fountains within Schlossgarten and Orangerie. In the days of black pedagogics, it also housed the Karzer of the University where students who had broken one of the myriad rules were thrown. Ultimately it became a badge of honor for every student to have at least one Karzer sentence to their name and they tried to "leave their mark" on the walls (despite that of course also being against the rules).
Built 1700–1704, it hosts the university's administration.
During the opening there is also an open air ice rink on the other half of the square (Marktplatz).
One of the 3 stages of the Stadttheater, which is the oldest Baroque theatre in Southern Germany - built in 1719. It is worth visiting, even if you don't understand German at all. Some plays and performances are held in the other locations. Given Germany's propensity to subsidise "high culture", tickets are very affordable indeed.
Especially popular amongst students and other young folks on nice weather and is used for sunbathing and playing; it also offers a lot of benches.
A nice place for a walk especially in rainy weather or winter. Visit the greenhouses. The garden offers an artificial stalactite cave, called Neischl-Grotte (which however is not always open).