Etymology
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mentor (n.)

"wise adviser, intimate friend who also is a sage counselor," especially of one who is young or inexperienced, 1750, from Greek Mentor, friend of Odysseus and adviser of Telemachus (but often actually Athene in disguise) in the "Odyssey." The name perhaps ultimately means "adviser," because in form it is an agent noun of mentos "intent, purpose, spirit, passion" from PIE *mon-eyo- (source also of Sanskrit man-tar- "one who thinks," Latin mon-i-tor "one who admonishes"), causative form of root *men- (1) "to think." Compare monitor (n.). Often capitalized, even in the general sense, into mid-19c. The general use of the word probably is via later popular romances, in which Mentor played a larger part than he does in Homer. Related: Mentorship.

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mentor (v.)

"serve as a mentor to," 1888, from mentor (n.). Related: Mentored; mentoring.

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adviser (n.)
1610s, "one who gives advice," agent noun from advise (v.). Meaning "faculty assigned to mentor students" is from 1887. Meaning "military person sent to help a government or army in a foreign country" is recorded from 1915. Alternative form, Latinate advisor, is perhaps a back-formation from advisory.
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guru (n.)

1806, gooroo, from Hindi guru "teacher, priest," from Sanskrit guru-s "one to be honored, teacher," from guru- "venerable, worthy of honor," literally "heavy, weighty," from PIE root *gwere- (1) "heavy." Generalized sense of "mentor" is from 1940 (in H.G. Wells); sense of "expert in something" first recorded c. 1966 in Canadian English in reference to Marshall McLuhan.

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