Beautiful adaptations for the third Partita were created by Sergei Rachmaninoff for piano, Camille Saint-Saëns, Willy Burmester (in his 'Stücke alter Meister'), and Fritz Kreisler (for violin & piano), Adolf Grünwald & Otto Standke for cello/piano, and JS Bach for chorus & orchestra in his 'Wir danken dir, Gott, wir danken dir' (We thank thee, God, we thank thee) BWV 29 as well as for his Suite in E major for Lute, BWV 1006a.
Emil Kross offers the following in his edition.
Prelude: Generally every introduction to an important work is called a Prelude. Its form is free from any precise rhythmical division or specially contrasted symmetrical parts or movements, thus leaving perfect freedom to the composer's imagination; it is usually based upon a certain musical subject. Every note of this prelude must be well rounded and evennes must prevail; special care and neatness is required at the change of strings, more particularly with the alternating (bell-like) open string and melody-tone [such as measure 13].
Loure: A dance in 3/4 or 6/4 time, similar to the Italian Gigue.
Gavotte and Rondo: The Gavotte is a French dance in common time (C).