How did universities develop in the middle ages?

During the Early Middle Ages, there were schools in many cities, some of which dated from the Roman Empire. Many of these schools were just collections of teachers and students, without any particular formal structure, and certainly not granting degrees anyone could recognize. Nevertheless, some cities were so well known for their schools that people travelled great distances to them for the educations they could get. Often there were competing teachers in the same city, teaching the same subjects.
In time, it became necessary for the teachers to organize to deal with competition, and so they followed the model of the medieval guilds, which had apprenticeships, followed by a journeyman status, then master and perhaps grand master. Since these grades were regulated, they could be recognized. So the new schools could grant degrees, including the bachelor's, which was equivalent to journeyman, and the master's. The doctorate was a licence to teach, and was not originally considered higher than a master's degree.
The first Western University was the University of Bologna, which is said to have been started in 1088. Due credit has to be given to earlier universities in other places since, for example the University of Constantinople had been operating since 425, and these may have provided a template to use to design the education.
As universities began to be chartered by the popes and monarchs, it became necessary to standardize education and make their degrees transferable. This was done in a papal bull in 1233.