The origin of the modern university system can be most directly traced to the universities of Oxford and Cambridge. Though predated by the University of Bologna and some other institutions, Oxford and Cambridge originated methods of organization and instruction which most directly informed the contemporary model of the university seen in the west, whose mission is the propagation, preservation, and creation of knowledge.
Originally, individual masters would take pupils for an extended period of instruction. These pupils would eventually be graduated and, after several years in the world, could return to be made masters in their own right. This three level hierarchy (pupil to bachelor to master) was modeled after the three level hierarchy of medieval trade guilds (apprentice to fellow to master). Early instruction was mostly limited to divinity and law.
Over time, the proliferation of masters gave rise to unscrupulous characters unqualified to give instruction. Reputable masters, therefore, banded together as universities. Now, the students of masters would have to be examined by the common institution of the university in order to be graduated, helping to ensure the quality and accuracy of instruction. Simultaneously, masters would retain associates—called fellows—to aid instruction of the growing bodies of students. A group of a mater, fellows, and students came to be known as a college.
Remnants of this medieval mode of organization are still in evidence at Oxford and Cambridge, which are divided into non-instructional "colleges" each headed by a master and deputized by fellows. While, over time, the duties of teaching have gradually been assumed by the university in its corporate capacity, the colleges remain as the basic building block of these two oldest of universities.