This monograph presents the theoretical groundwork for a performance of two Suites for Unaccompanied Cello by Johann Sebastian Bach on the baritone saxophone, through a mixture of interpretation and improvisation. By reviewing the existing literature on the interpretation of baroque music and through a careful study of both suites, choices as to how to interpret the suites as written on the saxophone were explained. The process of improvising within the suites is documented through the combination of a historic overview of improvisation in the baroque era and the analysis of the challenges presented by original compositions. Several key conclusions are presented which contribute to the existing literature in both the domains of interpretation and improvisation.