This piece is the second movement of J.S. Bach's 3rd orchestral suite in D major. The movement is an Air (Aria in Italian) which is famously referred to as "Air on a G String," because of German violinist August Wilhelmj's (1845–1908) arrangement where the first violin is transposed an octave lower and performed entirely on the instruments G string. It's absolutely one of my favorite pieces. The transcription I'm playing from is from A. Franzi. If you know the original score, or Wilhelmj's score you may notice some octave changes in the counterpoint, but I think the general feeling of the song translates well to the guitar with this arrangement.