  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.
