The first letter of the
Greek alphabet, written capital Α and lower case α , the HTML codes for which are Α and α . The upper-case letter is the same as a Roman A, and the lower-case one is similar to a handwritten
a, but written in a single loop from upper right, clockwise, down to lower right. Non-Greeks (e.g. mathematicians using it as a symbol) often exaggerate the lateral stretching of this, making it look like a fish, or the 'is proportional to' symbol. This should be avoided.
It comes from some Semitic alphabet, traditionally the Phoenician, pronounced something like the Hebrew name aleph, and meaning an ox. It originated as a picture of an ox's head. (Turn it on its side to see a triangular snout.) In Semitic languages it represents the glottal stop sound, but this not occurring in Greek it was used for the vowel A. Of course it gave rise to the Roman letter A (via Etruscan).
In Ancient Greek it had two values, long and short; in Modern Greek it retains the same vowel quality but there is no longer any distinction of length. It is the same sound as the A of most European languages. In English, A usually has a different sound (as in mat or mate), but the A of father is about the Greek long sound. The short sound is that of mutt for most southern British and Australasian speakers. (The American version of mutt is less accurate, but is still probably the closest in that accent to Greek short α.)
The length of the letter alpha was not marked in writing. However, with the introduction of accents by Aristophanes of Byzantium in the later classical period, came some marking, because the circumflex accent can only appear on long vowels. But alpha with acute or grave is ambiguous.
In Attic, the dialect of Athens in the classical period, long α was replaced by η eta in many circumstances. This had a long sound around those of English man or mare. But other dialects kept the A sound. Thus you get doublets such as Athena and Athene. This applied in particular to the feminine singular ending of first declension words. However, in Latin the corresponding ending is short -a, so it was easier to borrow Greek words into Latin with the A form.
There are two exceptions to this change of ending: it did not take place after a vowel (e.g. historia 'research'), or R (e.g. orkhestra). There is an exception to these: you would therefore expect kora for 'girl', the original vowel retained next to the R, but even in Attic this word was κορη korê, because it was originally korwa, and W was lost in pre-classical Greek after the Attic A-shifting rule applied.
It took part in three diphthongs, ai, au, aai. The first two were as in aisle and house. I delay discussion of aai. In Greek after the classical period, ai changed to an E sound (as in met), and au changed to AV, or (finally and before voiceless sounds) AF. These are the Modern Greek values.
These two were borrowed into Latin as the closest Latin sounds ae, au. So Aiskhylos became Aeschylus. Note that this is in no way inaccurate, or less correct than Aiskhylos: it is a transcription into the closest letters of the Roman alphabet (plus a Latin ending). Since classical Roman times, Latin changed, gave rise to French, was borrowed into English, and English changed. The Latin diphthong AE changed to a long E sound, then in the Great Vowel Shift of around 1500 this became the modern English EE sound: giving SEEza and EESkilus for Caesar and Aeschylus. The Latin AU also changed to a long O, and that's roughly what we use today.
Long diphthongs are comparatively rare in languages, though Thai has them in abundance. The ancestor of Greek, Proto-Indo-European, had aai, aau. I'm not sure what happened to aau, I shall have to look up my book for that one, but aai existed in the classical period, written ΑΙ, same as short ai. The iota element disappeared in the later classical period. With the appearance of lower-case letters and accents in the post-classical period, the silent iota came to be written small underneath the letter, and is called iota subscript, except at the beginning of a word, such as Αιδης (Hades), where it was retained in-line or adscript.
Greek letters were used as numerals, with a stroke by them, so α' was 1.