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The deep knowledge entailing understanding (think "carnal k." in English) and what you get from a detailed investigation is γνῶσις (gnôsis).
A more intellectual variant entailing expertise is ἐπιστήμη (epistēmē); mastery (from "standing on it").
An acquired knowledge, so, something you learn, education, is μάθημα, μάθησις (mathēma, ...
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