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Borrowed from Latin Sōl.

Shortening.

From Glover's solmization, from Middle English sol (“fifth degree or note of Guido of Arezzo's hexachordal scales”), Italian sol in the solmization of Guido of Arezzo, from the first syllable of Latin solve (“wash away”) in the lyrics of the scale-ascending hymn Ut queant laxis by Paulus Deacon.

Learned borrowing from Old French sol (“French coin”) (modern French sou), from Latin solidum, the accusative singular of solidus (“Roman gold coin; (adjective) solid”). Doublet of sold, soldo, solid, solidus, sou, and xu.

PIE word *sóh₂wl̥ From Spanish sol (“sun”), from Latin sōl (“sun”), ultimately from Proto-Indo-European *sóh₂wl̥ (“sun”). Doublet of Sol and sol, directly from the Latin.

From Latin sōl (“sun”); see further at etymology 3. Doublet of sol from Spanish.

Sense 1 (“type of colloid”) is derived from -sol (in words like alcosol and hydrosol), an abbreviation of solution. Sense 2 (“solution to an objection”) is derived directly from solution.