In Scotland, Edinburgh University was established in 1582. For class lists and matriculation records, the archivist at the actual university itself has to be contacted. There is a fee for the search. The archives cover for 1587 to 1888.
St Andrews in Scotland, has alumni printed for 1413 to 1579.
Glasgow University graduates are in a list compiled in A Roll of the Graduates of the University of Glasgow 1727-1897 by W. Innes Addison, Glasgow, 1898.
Aberdeen University has a web page with an excellent guide on all their genealogy sources: http://www.abdn.ac.uk/diss/docu/facts/sgc/fssgc11.pdf. Aberdeens history began in 1566.
Moving down to England now, the two universities, Oxford and Cambridge, were to dominate the scene until the 18th century.
All known students and holders of office that attended Cambridge are listed in the 10 volumes that make up Alumni Canatabrigiensis. Compiled by J. and J. A. Venn using various sources form the university records, it gives a rare opportunity to glean biographical information about your ancestor and his family. Each entry can offer a varied amount of information, ranging from birth date; place of birth; other schools attended; occupation; parents names; spouses name; siblings names. For anyone with well-educated ancestors, particularly if they are of the legal profession, clergy, or medical, both the Cambridge and the Oxford universities archives should be searched. The Cambridge alumni is online at Ancestry.co.uk, and searching the indexes are easy. The Society of Genealogists in London also has a full, printed set of the alumni. Considering the Cambridge alumni covers over 180,000 names, it is a of valued historical importance. The records from the university date as far back as the mid 1200's.
Oxford University, has its former graduates listed in Alumni Oxonienses by Joseph Foster, covering the dates 1500-1886. Equally full of information on the students' life pre-university and after, including their parents, date and place of birth, and educational achievements. It is in eight volumes, and the Society of Genealogists in London has a full set of these works. They do offer a search for a small fee of both the Oxford and the Cambridge works and can be contacted via their web site: Society of Genealogists, UK
The society does hold a collection of university and school registers, so its worth checking their online catalogue to see if they have any records in printed sources