I just break out laughing from sheer happiness every time I hear this. Nina Simone was training to be a concert pianist when she diverted into jazz. Here she puts all her abilities together with stylish vocals around a fast-tempo baroque instrumental where she improvises around some J.S. Bach chops. She was 25 when she introduced this in 1958. The song had been around for 30 years or so, but I think she pretty much owned it after this version.
There's a recording where you can see her performing this live, but it's a little shorter and of lesser sound quality than this one.
Mods, that's a link to the legitimate youtube post; no copyright problems here.
Love or leave me - Nina Simone - YouTube