Ingolstadt has two traditional Bavarian beer festivals (think Oktoberfest in small) lasting ten days each. The first and bigger one starts the Friday before Pentecost and is therefore known as the Pfingstfest. Herbstfest (autumn festival), the second one, starts on the Friday before the last Sunday in September, running in parallel to the second week of Oktoberfest. You can find beer tents, food, rides, games and stalls. It is a bit more traditional than Oktoberfest and not as bustling, but in the evenings (especially on Friday and Saturday) the beer tents become full blown party areas.
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Asam Church
Hidden in the narrow streets of the historic city centre, this is a jewel of baroque art, especially the fresco on the ceiling.
City Museum
Built 1425-1525 by Louis IX, Duke of Bavaria (aka Louis the Rich), this is the biggest church of Ingolstadt. Late Gothic architecture, the tomb of famous Ingolstadt scholars and the artistic interior make it a renowned place for visiting.
Dating back to 1234, this church is the oldest building in Ingolstadt.
Bayrisches Armeemuseum
The museum is separated into two locations. The Neues Schloss, a former duke's residence and part of the city wall, hosts a collection of military artefacts from different eras as well as a bunch of replicas. The Reduit Tilly, a part of the former state fortress in Klenzepark hosts a World War I exhibition. The latter is a very interesting and well structured museum, with exhibits and documents from the era and some short films which summarise the history. The Army Museum is being renovated in 2019, so some parts may be closed. Many of the captions are in German and they have something of a pro-Bavarian and politically conservative slant but the original exhibits are interesting even if you don't subscribe to their view of history.