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Notes in italics from Oxfordshire by Jennifer Sherwood and Nikolaus Pevsner (1974)
Yale University Press, New Haven and London.

The Divinity School must have been begun about 1420 ... the chief benefactor was Humphrey Duke of Gloucester, and it was due to him that the building was increased from one to two storeys for housing his library ... The building was complete by 1490, after it had been decided c.1480, and as an afterthought, that the Divinity School proper was to be vaulted.  ...

We can regard it as certain that the master of the masterly vault was William Orchard ... The vault is one of the marvels of Oxford, but to speak of it, one has to start by describing the two end walls. They each have three blank arches with straight shanks and buttress-shafts between. The middle arch is narrower and lower. The areas are panelled, and a sweeping four-centred super-arch comprises the two. For the vault is first of all a matter of four strong transverse arches plus the two wall arches. About half-way up they have a pair of pendants each, and it was the pride of that ingenious man William Orchard to let his whole vault with all its complicated ribs appear to issue from these pendants, which of course for structural reasons it can't. In fact the pendants are just bold arch voussoirs, and the vault is a lierne-vault with its weight pressing on the arches, the outer walls and the buttresses. The vault is very much like a fan vault, but it isn't, as the ribs are too prominent. So a lierne-vault it ought to be called. It has innumerable bosses. ... In addition there are statuettes under canopies, tiny ones on the pendants and larger ones along the two wall arches, eight on each. Over the middle W arch is the Virgin. ...

First picture: Boss of King Edward IV. Second picture: Boss of the architect William Orchard (centre of picture) 

The Divinity School is a rectangle, five bays long. It has a base frieze of quatrefoils, six-light windows and four-centred arches and panel tracery, panelled buttresses to the N ..., and twice as many upper, i.e. library, windows, each transomed and of two lights. Then follows the usual frieze of carvings, battlements and pinnacles. The N doorway is an insertion of 1669. This is a remarkable date; for it is decidedly Gothic and looks with its ogee gable and finial fifty years later. The doorway was inserted by Christopher Wren to form a processional route through to his Sheldonian Theatre entrance opposite. On the inside is his crest.
The projections to the E and W which give the building its H-shape are later. The eastern one is the Proscholium or vestibule of 1610-12, now part of the Bodleian, ... The Proscholium has much bare wall, divided by four elegant friezes of little pointed arches. ... The rather bleak pointed portal to the W looks early C18 (below).

The western (projection) houses convocation and Chancellor's Court and dates from 1634-7. The Convocation projection ... has no friezes. Fine classical portal to the E, looking - this one - 1669 or so indeed(below). Rusticated surround, Doric pilasters, segmental pediment with garlands.

Looking south from inside the Divinity School towards the Radcliffe Camera and St Mary's Church.