Georgian, Armenian and Azerbaijani are not related to each other. Neighbours for centuries, and still three separate language families — with three separate scripts to match.
Georgian belongs to the Kartvelian family, which has no proven relatives anywhere. Armenian is its own lone branch of Indo-European. Azerbaijani is Turkic, close enough to Turkish that the two are broadly mutually intelligible. Cross a border here and you are not changing dialect — you are changing everything.
Georgian uses mkhedruli, thirty-three rounded letters with no capitals, in daily use for roughly a thousand years. Armenian has its own alphabet from the fifth century, created deliberately and still used unchanged. Azerbaijani has switched three times in a century — Arabic, then Cyrillic, then Latin since the 1990s — so older signs and newer ones can look like different languages.
Russian still works with anyone over forty, and is often the common language between the three countries themselves. English is widespread among younger people in Tbilisi, Yerevan and Baku, and thins quickly outside the cities. Learning to read the numbers and a handful of menu words goes further than it sounds.
What to eat once you can read the menu: food of the region.