What do we call a medieval school of higher learning?

The story behind the answer

Medieval institutions of higher learning emerged in the 12th–13th centuries as self-governing corporations (universitates) of masters and students. They offered advanced study beyond cathedral and monastic schools, organizing teaching, granting degrees (bachelor, master, doctor), and standardizing curricula. Instruction centered on the liberal arts (trivium and quadrivium) before specialization in law, medicine, or theology.

Famous examples include Bologna (noted for law), Paris (theology and arts), and Oxford. These centers operated in Latin, used lectures and disputations, and often enjoyed charters and privileges from popes or kings, including clerical legal status. Their guild-like structure and degree system laid the foundation for the modern university model that still shapes higher education today.