An universiteit is a university.
In the medieval period, the area which is now known as the Netherlands did not have its own universities. People who wanted to pursue academic studies had to go to Paris, Cologne, Oxford, Bologna, or further afield. In 1425, the University of Louvain was founded in modern-day Belgium. Leiden has the oldest university of the Netherlands, founded in 1575. Other places that had universities were Franeker, Groningen, Utrecht, Harderwijk, and Nijmegen. Leiden, Groningen, Utrecht, and Nijmegen still have universities today, and several more have been founded since 1800.
Several early registrations of students have been published. See Oude Koektrommel for links.

Library of the Leiden University, 17th century. Credits: Special Collections Leiden, via Delpher.