The paper introduces harmonic polylogarithms (HPLs), a generalization of Nielsen's polylogarithms. HPLs satisfy a product algebra and are closed under transformations of their arguments, such as $ x = 1/z $ and $ x = (1 - t)/(1 + t) $. Their expansions and Mellin transforms involve harmonic sums. HPLs are defined recursively and can be expressed in terms of logarithmic and dilogarithmic functions for low weights. They are useful for evaluating Feynman diagrams and other physical quantities in quantum field theory. The paper discusses their properties, including their behavior at specific points, their algebraic structure, and their relation to harmonic sums. It also presents identities between HPLs of related arguments, such as $ x \rightarrow -x $, $ x \rightarrow x^2 $, $ x \rightarrow 1 - x $, and $ x \rightarrow 1/x $. These identities are essential for simplifying and evaluating HPLs in various contexts. The paper also addresses the numerical evaluation of HPLs and their Mellin transforms, which are closely related to harmonic sums. The results show that HPLs provide a powerful tool for expressing results of moment calculations in deep inelastic scattering and other high-energy physics processes.The paper introduces harmonic polylogarithms (HPLs), a generalization of Nielsen's polylogarithms. HPLs satisfy a product algebra and are closed under transformations of their arguments, such as $ x = 1/z $ and $ x = (1 - t)/(1 + t) $. Their expansions and Mellin transforms involve harmonic sums. HPLs are defined recursively and can be expressed in terms of logarithmic and dilogarithmic functions for low weights. They are useful for evaluating Feynman diagrams and other physical quantities in quantum field theory. The paper discusses their properties, including their behavior at specific points, their algebraic structure, and their relation to harmonic sums. It also presents identities between HPLs of related arguments, such as $ x \rightarrow -x $, $ x \rightarrow x^2 $, $ x \rightarrow 1 - x $, and $ x \rightarrow 1/x $. These identities are essential for simplifying and evaluating HPLs in various contexts. The paper also addresses the numerical evaluation of HPLs and their Mellin transforms, which are closely related to harmonic sums. The results show that HPLs provide a powerful tool for expressing results of moment calculations in deep inelastic scattering and other high-energy physics processes.