A Look up A at Dictionary.com
first letter of the Roman alphabet, based on Greek alpha (see alpha). In music from c. 1600 as the name of the sixth note of the natural scale; it is the note given by a fixed-tone instrument (usually oboe or organ) to which all the instruments of an orchestra are tuned. As a blood type, 1926, denoting A agglutinogens. The A side of a two-sided record (by 1962, see side (n.)) held the material chosen for promotion. A-bomb, short for atom bomb, was in newspaper headlines by Aug. 8, 1945.
a (1) Look up a at Dictionary.com
indefinite article, form of an used before consonants, mid-12c., a weakened form of Old English an "one" (see an). The disappearance of the -n- before consonants was mostly complete by mid-14c. After c. 1600 the -n- also began to vanish before words beginning with a sounded -h-; it still is retained by many writers before unaccented syllables in h- or (e)u- but is now no longer normally spoken as such. The -n- also lingered (especially in southern England dialect) before -w- and -y- through 15c.

It also is used before nouns of singular number and a few plural nouns when few or great many is interposed.
a (2) Look up a at Dictionary.com
as in twice a day, etc., a reduced form of Old English an "on" (see on (prep.)), in this case "on each." The sense was extended from time to measure, price, place, etc. The habit of tacking a onto a gerund (as in a-hunting we will go) was archaic after 18c.