From BiblePortal Wikipedia

Webster's Dictionary [1]

(1): ( n.) A particular power and practice of poetry.

(2): ( n.) To think closely; to study in silence; to meditate.

(3): ( n.) One of the nine goddesses who presided over song and the different kinds of poetry, and also the arts and sciences; - often used in the plural.

(4): ( n.) To wonder.

(5): ( n.) Contemplation which abstracts the mind from passing scenes; absorbing thought; hence, absence of mind; a brown study.

(6): ( n.) To be absent in mind; to be so occupied in study or contemplation as not to observe passing scenes or things present; to be in a brown study.

(7): ( n.) Wonder, or admiration.

(8): ( n.) A gap or hole in a hedge, hence, wall, or the like, through which a wild animal is accustomed to pass; a muset.

(9): ( v. t.) To think on; to meditate on.

(10): ( v. t.) To wonder at.

(11): ( n.) A poet; a bard.

King James Dictionary [2]

MUSE, n. s as z. L. musa.

1. Properly, song but in usage, the deity or power of poetry. Hence poets in modern times, as in ancient, invoke the aid of the Muse or Muses, or in other words,the genius of poetry.

Granville commands your aid, O Muses, bring,

What Muse for Granville can refuse to sing?

2. Deep thought close attention or contemplation which abstracts the minds from passing scenes hence sometimes, absence of mind.

As in great muse, no word to creature spake.

He was fill'd

With admiration and deep muse to hear

Of things so high and strange.

MUSE, s as z. L. musso and mussito, to mutter or murmur, to demur, to be silent. The Greek signifies to press, or utter sound with the lips compressed. The latter verb belongs to a sound uttered through the nose or with close lips, or of the same family, L. mussitatio. The word then primarily denotes what we call humming, to hum, as persons do when idle, or alone and steadily occupied.

1. To ponder to think closely to study in silence.

He mused upon some dangerous plot.

I muse on the works of thy hands.  Psalms 143

2. To be absent in mind to be so occupied in study or contemplation, as not to observe passing scenes or things present. 3. To wonder.

Do not muse of me.

MUSE, To think on to meditate on.

Holman Bible Dictionary [3]

 Psalm 143:5 Luke 3:15