The harmonic polylogarithms (hpl's) are introduced. They are a
generalization of Nielsen's polylogarithms, satisfying a product algebra
(the product of two hpl's is in turn a combination of hpl's)
and forming a set closed under the transformation of the arguments
\( x=1/z \) and \( x=(1-t)/(1+t) \). The coefficients of their expansions
and their Mellin transforms are harmonic sums.