What is the greek or latin word of archeology?

There isn't a single Greek or Latin word that directly translates to "archeology" as we understand the term today. The field developed later than the classical languages. However, the word is built from Greek roots:

* ἀρχαῖος (archaios): meaning "ancient," "old," or "primitive"

* λόγος (logos): meaning "word," "speech," "reason," or "study"

Therefore, "archeology" is a modern word built from these classical Greek components to mean, roughly, "the study of ancient things."