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The University of Zurich does not have any dorms, but here are some of the cheaper accommodation options in Zurich:
The following website will point you to some further budget accommodation options:
Reasonably priced regular hotels may be found through the usual travel booking websites and apps.
It might also be worth checking Airbnb, especially if you are travelling in a group. Finally, the Couchsurfing platform might also be an option (https://www.couchsurfing.com/).