After reading a little bit about glyphs, and their importance in typography, I am left wondering whether the letter α would count as a glyph in Ancient Greek, or whether only diacritical marks such as accents and breathing marks would count as glyphs. Could anyone answer this question for me? Are there multiple answers depending on context (e.g. typography in the pre-computing era versus typography in computing) or would α in Greek and the letter a in English be universally recognized as glyphs?
A glyph is a single unit of writing, which has a meaning within an agreed-upon method of communication. So for example, i is a single glyph, while the dot part of it isn't (since the dot means nothing on its own).
Note that glyphs are defined within a method of communication: in Turkish, for example, i with a dot and ı without a dot are distinct glyphs, because they have distinct meanings within Turkish. In English ı only has meaning as part of i, so it's not its own glyph.
In the typesetting days, ligatures were also often treated as glyphs, because they were single blocks of type. Nowadays that's less common, except in cases like the German ß (originally a ligature of ſz) where they've taken on their own meanings.