The first writing in Greece got started in the Late Bronze Age, and it was a hieroglyphic kind of writing like Egyptian hieroglyphs but using different signs. We call this writing Linear B. Each Linear B sign stood for a syllable. You needed a lot of signs, so it was hard to learn to write this way. Only specialist scribes could do it. They used Linear B writing mainly for taxes and accounting.
Then there was a Dark Age, about 1000 BC. There were no more scribes, and nobody in Greece knew how to write anymore. Nobody could afford to educate scribes. Then about 800 BC Phoenician traders came to Greece and brought news of a new way to write: the alphabet.
In West Asia, the alphabet was easy to learn because each letter was a picture of a word that started with that letter. R was a picture of a “rosh,” a head. The Greeks spoke Greek, which wasn’t even vaguely related to Aramaic. The pictures didn’t help them with the sounds. But they still found the alphabet pretty easy to learn, and soon people in Greece were using the alphabet not just for trading but also to write poetry and to write down the Iliad and the Odyssey. This may have been the first use of the alphabet to write literature instead of just for business.
In Greek though, vowels were more important than they were in Aramaic. People needed to be able to write more vowels than the Phoenician alphabet had. So Greek writers added a few more letters to the alphabet. They also changed the sound of a couple of letters that were not so useful to them: Waw became Upsilon, a vowel, and Q became Phi. To show that these were new, they moved them to the end of the alphabet. Also, while in West Asia people wrote from right to left, early Greek writers wrote “boustrophedon”, the way the ox plowed the field – one line from right to left, then the next from left to right, then back again. Because they were writing both ways, they also made the letters both ways, facing left or right.
Slowly this changed again, so that by about 600 BC, everybody in Greece was writing from left to right, instead of from right to left as they did in West Asia. Some of the letters ended up facing left, and others ended up facing right. Since the pictures didn’t mean anything to the Greeks, some letters even got turned on their sides, like S or A. By this time, in the Archaic period, Greek writing looked very different from West Asian writing, even though they had come from the same alphabet.
Learn by doing: learn to write the Greek alphabet and some words in Greek
More about the invention of the alphabet