The paper introduces harmonic polylogarithms (HPLs), a generalization of Nielsen's polylogarithms. HPLs are defined through a recursive integral definition and form a set closed under the transformation of arguments \(x = 1/z\) and \(x = (1-t)/(1+t)\). The coefficients of their expansions and Mellin transforms are harmonic sums. The authors study various properties of HPLs, including expressions for products of HPLs with the same argument, behavior at \(x=0\) and \(x=1\), and identities between HPLs of related arguments. They also explore special values and numerical evaluation, and show that the Mellin transforms of HPLs give harmonic sums. The paper provides algorithms for computing these transforms and discusses the algebraic structure of HPLs, including identities based on the shuffle algebra and triangle theorem. The results are useful for evaluating Feynman diagrams and have applications in quantum field theory.The paper introduces harmonic polylogarithms (HPLs), a generalization of Nielsen's polylogarithms. HPLs are defined through a recursive integral definition and form a set closed under the transformation of arguments \(x = 1/z\) and \(x = (1-t)/(1+t)\). The coefficients of their expansions and Mellin transforms are harmonic sums. The authors study various properties of HPLs, including expressions for products of HPLs with the same argument, behavior at \(x=0\) and \(x=1\), and identities between HPLs of related arguments. They also explore special values and numerical evaluation, and show that the Mellin transforms of HPLs give harmonic sums. The paper provides algorithms for computing these transforms and discusses the algebraic structure of HPLs, including identities based on the shuffle algebra and triangle theorem. The results are useful for evaluating Feynman diagrams and have applications in quantum field theory.