The title of this book, Mille Fabulae et Una, is an homage to that great story collection, the Alf Laylah wa-Laylah, usually known in English as the 1001 Nights or The Arabian Nights. Throughout their long history, Aesop's fables have regularly been infused with stories from eastern sources and, in turn, Aesop's fables have also traveled to the east, being adopted and transformed by Buddhist, Hindu and Islamic storytellers.
No one knows for sure just what eastern stories may have become incorporated into the Aesop's fable tradition already in ancient times. The similarities between Aesop's fables and the Buddhist jataka tales are tantalizing. There are hundreds of jatakas preserved in the Buddhist canon, and many of them contain plots and motifs that resemble the classical fables of Aesop. As to just who might have borrowed from whom, no one is really sure!
Another great storytelling tradition that originated in India is the Panchatantra, a set of nested stories-within-stories that interweave didactic tales with humorous jokes, similar in theme and content to Aesop's fables. In the European Middle Ages there were many translations into Latin of the stories from the Indian Panchatantra tradition, especially via the Arabic version known as Kalila wa-Dimnah. In addition to these literary translations, oral stories from the Middle East traveled back to Europe during the time of the Crusades, as in the eastern tales that can be found in the Exempla of Jacques de Vitry. The Panchatantra tales were later translated into English and other European languages during the Renaissance and early modern period, often under the name of Bidpai or with the title Hitopadesha.
For further reading on this topic, see Joseph Jacobs's history of the Aesopic fable in his edition of Caxton's Aesop, along with the notes and commentary provided by Thomas Crane in his edition of Jacques de Vitry, both of which are listed in the Bibliography (p. 429).