Converting Hue Sat and Lum to R G B and back

Hi. Can anyone provide me with an explanation of how to convert between rgb and hue sat lum colour values?

Really, I would like to know how they are related mathematically.

Thanks

There's an example in the archives. Basicly, the imbalance between rgb gives the saturation, the relation from r to b and r to g gives the hue and (r+g+b)/3 is the lum aka brightness.