There are hundreds of Wizards within Unseen University (although at UU, the term "within" must be considered in several extra dimensions. The almost infinitely extensible corridors and the flexibility of space itself make an accurate census difficult.) They form an intricate hierarchy of Orders, Levels and Titles jostling for influence, prestige and a seat nearer the buffet,since there's no suggestion of anyone drawing a salary. Power and prestige reside with the Archchancellor and are grudgingly allowed to trickle in small and precisely measured amounts down the hierarchy, stopping short at the Egregious Professor of Cruel and Unusual Geography, who is currently its lowest, least, and most despised, member. (Much to the relief of Ponder Stibbons, who is beginning to realise how promotion happens around these parts). Supporting this cadre is a large maintenance, housekeeping, and especially kitchen staff.
Precedence in the academic hierarchy seems to run: Archchancellor, Vice-Chancellor (although there hasn't been one for decades), Dean, Dean of College, Chair or Head, Endowed Professor, Professor, Lecturer/Reader. The Librarian takes precedence if he wants.
We see a little more of the way the University hierarchy operates in The Science of Discworld III: Darwin's Watch, when in order to manipulate the Roundworld timeline, wrest control back from the Auditors of Reality and ensure the one possible universe happens where Charles Darwin writes the right book, Ridcully scours the university for every able-bodied wizard who is capable of being sent on a mission. As over two thousand changes are needed, and most wizards are sent on two or more missions, it is possible to infer that there are between five hundred and a thousand wizards at the University with some sort of arcane speciality and maybe even tenure, most of whom are not seen except at mealtimes.
The group of senior staff at Unseen University who at least in theory lead, define its direction, set policy, pay the bills, hire and fire, have eight-course Guild dinners on behalf of the university, deal with the Patrician, and in extreme cases where there simply isn't any alternative or Room 3b isn't available, interact with students. The Council usually includes:
- the Archchancellor, currently Mustrum Ridcully
- the Dean, recently departed
- the Chair of Indefinite Studies
- the Lecturer in Recent Runes
- the Senior Wrangler
- the Bursar
- the Librarian
- Ponder Stibbons, as:
Such wizards would not normally be invited to Council meetings, but their skills and specialties may make them occasional ex-officio members.
- the Head of Post-Mortem Communications
- the Professor of Applied Anthropics (mentioned in Hogfather)
- the Professor of Astrology (in The Light Fantastic)
- the Professor of Revolvings / Professor of Extreme Horticulture
- the Professor of Recondite Architecture and Origami Map Folding
- the Professor of Recondite Phenomena
- the Professor of Logic
- the Prehumous Professor of Morbid Bibliomancy
- the Egregious Professor of Grammar and Usage
- the Lecturer in Applied Astrology (in Equal Rites)
- the Lecturer in Creative Uncertainty (mentioned in The Last Continent)
- the Lecturer (?) in Vindictive Astronomy (mentioned in The Truth, title implied but not specified)
- the Reader in Woolly Thinking (mentioned in Interesting Times. Woolly thinking is like fuzzy logic, only more so)
- the Reader in Esoteric Studies also known as the Reader in the Lavatory (mentioned in Soul Music)
- the Chair of Oblique Frogs
- the Professor of Criminology
- Rincewind, as:
- the Chair of Experimental Serendipity
- the Chair for the Public Misunderstanding of Magic
- the Egregious Professor of Cruel and Unusual Geography
- the Fretwork Teacher
- the Health and Safety Officer
- the Lecturer in Approximate Accuracy
- the Professor of Slood Dynamics
- the Professor of Virtual Anthropology
Then we have to consider the temporarily deceased wizards who are taking a sabbatical for a year or so: as this class of wizard (temporarily) physically exists only as a knitted sock-puppet in a jar in the cupboard (don't ask - it's in Going Postal) then this would preclude their being active members of the Faculty. In this category we have:-
along with other dead wizards who would like to take a more active role, but whom Ridcully would not want turning up at a Faculty meeting.