Muse
late Middle English: from Old French, or from Latin musa, from Greek mousa .
wiktionary
From Middle French muse, from Latin Mūsa, from Ancient Greek Μοῦσα(Moûsa).
From Middle English musen, from Old French muser.
From French musse. See muset.
etymonline
muse (v.)
"to reflect, ponder, meditate; to be absorbed in thought," mid-14c., from Old French muser (12c.) "to ponder, dream, wonder; loiter, waste time," which is of uncertain origin; the explanation in Diez and Skeat is literally "to stand with one's nose in the air" (or, possibly, "to sniff about" like a dog who has lost the scent), from muse "muzzle," from Gallo-Roman *musa "snout," itself a word of unknown origin. The modern word probably has been influenced in sense by muse (n.). Related: Mused; musing.
Muse (n.)
late 14c., "one of the nine Muses of classical mythology," daughters of Zeus and Mnemosyne, protectors of the arts; from Old French Muse and directly from Latin Musa, from Greek Mousa, "the Muse," also "music, song," ultimately from PIE root *men- (1) "to think." Meaning "inspiring goddess of a particular poet" (with a lower-case m-) is from late 14c.
The traditional names and specialties of the nine Muses are: Calliope (epic poetry), Clio (history), Erato (love poetry, lyric art), Euterpe (music, especially flute), Melpomene (tragedy), Polymnia (hymns), Terpsichore (dance), Thalia (comedy), Urania (astronomy).