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Photo: Jan Beckendorf, CC BY-SA 2.0 via Wikimedia Commons
The old university in the old city.
Heidelberg University, officially the Ruprecht Karl University of Heidelberg, is a public research university in Heidelberg, Baden-Württemberg, Germany. Founded in 1386 on instruction of Pope Urban VI, Heidelberg is Germany's oldest university and one of the world's oldest surviving universities; it was the third university established in the Holy Roman Empire after Prague (1347) and Vienna (1365). Since 1899, it has been a coeducational institution.
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The university has its own museum, in the main building of the old campus. Visitors are able to view the Great Hall (when not in use), and the former "student jail".
It has 1712 Baroque construction with modern touches inside.
Theater und Orchester Heidelberg
Large theatre house, home also to the philharmonic orchestra. Concerts, music theatre, dance and other performances.
Palatinate Museum
This city-run museum contains interesting exhibits of items from Heidelberg's pre-history to modern times, and a fine-art collection. Audio guide available, including in English
The old armoury is now a student cafeteria (open to the public and offering good food and drinks at reasonable prices).
The Heiliggeistkirche (Church of the Holy Spirit) is only one of many large and small churches, but definitely the one with the most interesting history. During the Dark Ages, it was the shelter of the Bibliotheca Palatina, Germany's oldest library. The Bibliotheca was stolen and brought to Rome but eventually returned in pieces. Today, parts of it can be visited in the University Library (also the oldest and probably the most valuable of its kind in Germany), which is situated close to the old university. You can get a great view of the Heiliggeistkirche, Old Town, and the Neckar river bridge from the castle (Schloss Heidelberg).