Answer:
The modern university was begun by students a thousand years ago who travelled south to Italy to obtain higher learning.
They clubbed together and hired entire inns, much cheaper than renting rooms individually. These inns became the first colleges.
Professors were hired by these colleges to give specified courses of instruction in their profession.
Some students had their own money, some were sponsored, some earned a living by tutoring other students.
This type of institution of learning was too good to leave in the hands of students: cities, enlightened despots, churches and benefactors took over existing universities and established new ones throughout Europe.
Subjects taught included Law, Medicine, classics: Latin, Greek, Hebrew. Theology was taught in religious establishments, there was moral and natural philosophy, and extensions to school subjects: Trivium (grammar, rhetoric, logic) and quadrivium (mathematics, geometry, music, astronomy).