I strongly believe that food is a fundamental part of a country's tradition, so which is the first culinary book ever written?
A collection of 26 Babylonian recipe tablets written in Akkadian from 1700BC have been deciphered. Here is an interesting newspaper article on the translations by a chef-turned-antiquarian:
Recipe tablets from the Yale Babylonian Collection, previously thought to contain pharmaceutical formulas, have been decoded by French Assyriologist and gourmet chef Jean Bottero. The three Akkadian tablets, dating to about 1700 BC, revealed, Bottero wrote in a description of his find, "a cuisine of striking richness, refinement, sophistication and artistry, which is surprising from such an early period. Previously we would not have dared to think a cuisine 4,000 years old was so advanced."
Wikipedia has a list, starting with:
The earliest collection of recipes that has survived in Europe is De re coquinaria, written in Latin. An early version was first compiled sometime in the 1st century and has often been attributed to the Roman gourmet Marcus Gavius Apicius, though this has been cast in doubt by modern research. An Apicius came to designate a book of recipes. The current text appears to have been compiled in the late 4th or early 5th century; the first print edition is from 1483.
Not as ancient as Babylonian recipe tablets from 1700 BC, but still I think they're worth a mention.
Archestratus of Gela, a "Sicilian-Greek gourmet" and poet of the 4th century BC, known as "the father of gastronomy" and "the Daedalus of tasty dishes", wrote a book on food very popular in antiquity. This work has been cited under different names: Gastrology, Gastronomy, Hedypatheia...
According to Wikipedia:
His humorous didactic poem Hedypatheia ("Life of Luxury"), written in hexameters but known only from quotations, advises a gastronomic reader on where to find the best food in the Mediterranean world.
... most of his attention is given to fish, although some fragments refer to appetizers, and there was also a section on wine.
The Dictionary of Greek and Roman Biography and Mythology also says that Archestratus had a teacher, Terpsion:
mentioned by Athenaeus as the first author of a gastrologia, giving direction as to the viands from which it was advisable to abstain.