Air on the G String is August Wilhelmj's arrangement of the second movement in Johann Sebastian Bach's Orchestral Suite No. 3 in D major. The original orchestral suite was generally believed to have been written by Bach for his patron Prince Leopold of Anhalt between the years 1717 and 1723. However, the oldest surviving score is later, dating from Bach's time in Leipzig. Current thinking is that the suite may well have been written in that city for performance by the collegium musicum around the year 1725. The title comes from violinist August Wilhelmj's late 19th century arrangement of the piece for violin and piano. By transposing the key of the piece from its original D major to C major and transposing the melody down an octave, Wilhelmj was able to play the piece on only one string of his violin, the G string.
Recently I heard an arrangement that was for the piano, it was simply titled Air.