I'll keep this limited to my field of knowledge, which is Early Modern Spain, but I hope more people will add answers about other places.

The University of Salamanca was founded in the early years of the 13th century, with the date of foundation generally accepted as 1218. This university gained a lot of notoriety in the realms of Spain and even abroad, specially thanks to the famous School of Salamanca, more commonly known in modern times as "Spanish School", as many of the great thinkers of the 16th century did not come from of Salamanca, but from the universities of Valladolid and of Alcalá as well, with great scholars such as Francisco de Vitoria, Francisco Suárez, Cristóbal de Villalón, and the other Cristóbal de Villalón. In that century, Salamanca, Valladolid, and Alcalá were prestigious universities, and were the only ones with the legal consideration of "major universities" (universidades mayores), denoting a certain primacy over other institutions such as Seville, Oñate, Osuna, or Santiago.

According to the statutes of the University of Salamanca from the period (Estatutos from 1564, 1584, and 1592), in order to be admitted to the university, one had to prove his competence in the Latin language in an exam before an academic tribunal of the university. Certifications from other universities were accepted, provided the candidate would provide two witnesses who would sign affidavits under penalty of perjury and fraud.

If you proved your sufficience in Latin, you would receive a certification, and with that paper you could enroll in any of the courses provided by the university, which were abundant. In Salamanca you could study Arts, Medicine, Astrology, Law, Canons, Theology, Mathematics, etc.

The enrollment fee was six maravedis per course, which is to mean per academic year, except for those studying Grammar (which is to say Latin, Greek, Hebrew), who would pay four maravedis. There was no fee for direct relatives of members of the university. Besides these fees, there were also "examination rights" which were the fees one had to pay in order to be examined at the end of the academic year, and also some other fees for the final exam that would allow you to receive the title of bachelor, licenciate, master, or doctor.

Medicine had its own particularities, as in order to enroll in Medicine studies one had to complete a bachelor in Arts first, which is to say three years of university education. Of course, in order to avoid fraud, all of the processes involved quite some paperwork, but that is par for the course.

So, let's say you want to study Medicine. First, you would need to prove your capabilities in the Latin language, and receive the according certificate from the university's secretary, previous presentation of the document issued by the academic tribunal. With that in hand, you would then enroll in the first year of a bachelor of Arts course, and receive a certification of enrollment, which would entitle you to the franchises, privileges, and immunities of the students of Salamanca. Having completed that first year of studies, you would get a certificate from the academic tribunal, which would allow you to enroll in the second academic year. With that in hand, you would go to the secretary, pay the fee, and be enrolled for a second year. Rinse and repeat. Having finished your three years, you would be subject to a final examination that would allow you to obtain the title of bachelor of arts. With the certification of your sufficiency, you would then go to the academic secretary, who would provide you with the official title.

With your title of Bachelor of Arts, then you would be allowed to enroll in the first year of Medicine. Etc etc until your final examination where you should prove before the profesdors your sufficience. That proven, certificate obtained, duties and fees paid, you would get your fancy title of Licenciado en Medicina (Graduate in Medicine).

Don't be fooled, as the certificate of being a graduate in Medicine was not enough to become a full physician. You should then start a two year apprenticeship with a certified physician, and after that you would be examined by the Tribunal del Protomedicato (academic tribunal of the College of Physicians).

This long story is the reason why I called into question the date of birth of Jerónimo Gómez de Huerta, normally given as 1573 but that is outright impossible, as in a book of his written in 1588 he appears as "Graduate in Medicine", which would be impossible at age 15. His actual date of birth is 1564, as I argue in a paper soon to be published. Huerta was a tad of a precocious genius, becoming a graduate in Medicine at age 24, which is a bit early for the period.