Texts and Transmissions tells me that the fundamental edition of Aulus Gellius’ Attic Nights is the editio maior of M. Hertz, Berlin, 1883-5 (2 vols). This is online in two volumes here(1883) and here (1885), although the title pages in these two PDF’s seem to have been exchanged. The Teubner text of C. Hosius (1903) involved no new work on the manuscripts, and the most recent full critical edition is the Oxford Classical Texts edition Noctes Atticae by P. K. Marshall (1968), 2 vols. Rene Marache has produced a Bude edition, Les Nuits Attiques
Some details of the transmission and publication of the text are accessible to all in Google books preview here of Leofranc Holford-Strevens Aulus Gellius: an Antonine scholar and his achievement, which seems to be an excellent volume indeed.
The Attic Nights are quoted a lot in ancient times, as such a compilation of anecdotes and learning was bound to be. Apuleius (De Mundo 13-14); Lactantius (Epit. inst. div. 24.5), Nonius and Ammianus Marcellinus and Macrobius in many places, and the Historia Augusta 28.1.1, together with Servius (Commentary on the Aenid 5.738, and on the Georgics 1.260 and Aen. 7.740) and Augustine in the City of God 9.4.
We have a fourth century manuscript, even, a palimpsest, written in rustic capitals and containing large parts of books 1-2 and some of 3-4. It also has the chapter headings for books 17-18 presented continuously, indicating that when new the codex originally contained all 20 books, with the headings at the front, immediately after the preface.
Incidentally I have complained before about the manner in which the unmeaning non-English word “lemma” is tossed around in classical studies, attached to a range of objects as a jargon word. In scholia it denotes the couple of words of quotation from the main text, to which the scholion relates. In dictionaries it means the word in its base form, nominative singular etc. But it seems that yet another use is found in Aulus Gellius studies, where “lemmata” means the index of chapter titles! To scholars I say: Enough! Stop using this word. It’s simply a barrier to ordinary people.
Back to the text of Aulus Gellius. It was transmitted in two halves; but instead of books 1-10 and 11-20, as we might expect, it has reached us in books 1-7 and 9-20. Book 8 is lost.
Books 1-7 are known to us from four manuscripts from France, of the 12-13th century. There are also quotations in a couple of anthologies.
Books 9-20 are known to us from three families of manuscripts. The first of these is a single manuscript written at Fulda in 836, as a group effort, on the orders of Rabanus Maurus for Servatus Lupus. But no-one ever seems to have copied it. There is a second family of four manuscripts, 9th, 10th, 12th century, plus one 15th century copy written by the great Florentine collector Niccolo Niccoli himself, probably from a 9th century ms., and which was the parent of all the renaissance copies, presumably because it was the easiest to read and most accessible. There is a third family of three manuscripts of the 12-13th century.
The two halves of the text were first put back together in the early 15th century. But one other important event took place then. Someone, somewhere — we don’t know who or where — found something present in no manuscript now extant. He found the chapter headings for book 8, the lost book; and he found the ending for book 20. These were added to the printed edition, and appear first in the edition in Venice in 1493. Hertz discusses this in vol.1 p.406, note; the italics are Hertz’ words, while the normal text is quotations from somewhat vaguely specified early editions. All they say is that the material came from an “old copy”.