Reference edition:

Abrégés des livres de l'histoire romaine de Tite-Live, vol. 34.1: «Periochae» transmises par les manuscrits (Periochae 1-69) ; vol. 34. 2:  «Periochae» transmises par les manuscrits (Periochae 70-142) et par le papyrus d'Oxyrhynchos, texte établi et traduit par Paul Jal, Paris 1984 (Collection des Universités de France).

The Periochae (from the Greek περιοχή, ‘summary’) are summaries of the 142 books that comprise Livy’s Ab urbe condita.  These brief epitomes have come to us mostly intact, with the exception of those for books 136 and 137. The length of the synopses varies greatly, e.g. from the three lines of book 135 to the three pages of books 48-49, but it is impossible to identify a single criterion that might have guided these compositional decisions: it may be observed that each periocha functions as an index and inventory of the chief events of Livy’s book, and thus serves both an informational and a didactic purpose. The synopses relate the most important events, while their order mostly follows the chronological sequence of the summarized book (Kornemann).  In the case of the Book 1, a double redaction has come down to us: the first (1a) contains a complete summary of the Livian book; the second (1b) starts at the midpoint of Ancus Marcius’ reign (Liv. 1.33).  Despite this, the latter coheres with and complements the rest of the corpus, and thus probably preserves the traces of another epitome of Livy that was later lost after being used to fill the initial lacuna of 1b (Sanders, Rossbach). 

The Periochae are preserved by various manuscripts. The oldest and most authoritative of these is Palatinus Latinus Heidelbergensis 894 (N), dating to the 9^th c., which also contains e.g. the epitome of Florus. The editio princeps dates to 1469, published by Sweynheym and Pannartz.  The work’s authorship is uncertain: still, chiefly due to the work of Wölfflin, it is possible to maintain that it was written by a single author. 

As regards the dating, it is now customary to accept the position of Bessone and Jal, who place the Periochae in the 4^th c. AD, both due to linguistic similarities to works of that age and, chiefly, because such a dating would align perfectly with the development of historiographical epitome as a genre, which reaches full bloom in this period.  [A. Balbo; tr. C. L. Caterine].