The history of student administration is complex. Today these affairs are handled by the University Registry but, in earlier periods, they were handled elsewhere.

Prior to 1791 each professor matriculated his own class. Students often attended more than one class. In 1791 and up until 1810, the students attending the literary and philosophical classes enrolled themselves in one continuous list, as did also the students attending the Scots and civil law classes. Medical students, previous to 1763, matriculated with each professor they attended. From 1810 all medical students were annually enrolled in one alphabetical list. From 1811 all the students annually enrolled themselves in one continued list and describe themselves as literary, medical or law students.

Previous to this date, the total number of the literary and philosophical students that have matriculated cannot be accurately known, from the circumstance of the greater number of them attending more than one class in the same session. From about the 1820s students were also matriculated according to faculty.

The matriculation of students was not so strictly enforced before 1809, so numbers are probably less than students who attended the College. In 1812 it was stated that every student must provide himself with a matriculation ticket, for which the fee was 10 shillings. Students at the time could enrol between 10am and 3pm in the Library which seems to have carried out this part of the matriculation process. It also stated that the entering of a name in the matriculation album was the only legal record of attendance in the University. Matriculation involved a different process for medical students.

As part of the process of matriculation a solemn promise of obedience and good behaviour was taken called a Sponsio Academia and is annually prefixed to the list of students who matriculate or enrol themselves each year in the album. It appears that the Sponsio had previously been taken in the Great Hall of the College, accompanied by an exhortation from the principal. The Sponsio then appears to have been part of signing the matriculation album prefixed to the annual lists of students from 1762. The Sponsio did not involve any religious test.