But the Greeks didn't invent it. Some Greek genius who knew the Phoenicians' language adopted their 22-letter alphabet to write Greek. The Phoenicians had no signs for vowels, so the Greek altered the sound of some letters and invented others, placing the new letter omega at the end. By early in the 8th century BC Greeks throughout the Mediterranean were using variants of this alphabet. Its Phoenician origin is proved by the order of the letters - similar to alphabets used in Sinai - and by the names of many of the letters, which mean nothing in Greek, but do in Semitic languages. Alpha means a bull, beta a house etc.
The Romans dropped a few Greek letters including omega, and made a slight alteration to the order.
Harrow on the Hill, Middlesex