As is known, an objective assessment of scientific activity is one of the most difficult problems, in terms of the relationship within itself as well as with society. However, for many decades, the significance of scientists' contribution to the development of the corresponding branch of science was assessed by the scientific community only by meaningful qualitative criteria, wherein the principle and mechanism of such an assessment was actually intuitive and defied quantitative description. That is why the urgent task was undertaken to create a system for evaluating scientific activity based on some objective indicators of the activity of a particular scientist
in search of such criteria, in the 1970s-1980s, the term "citation index" appeared. Although a close examination of this indicator revealed its limitations and in a number of cases even inadequacy in assessing scientific activity, it has nevertheless since the 1990s gained very wide popularity in the scientific community. This has contributed to the emergence of numerous works aimed at finding new and ideal indicators for assessing publication activity (so-called bibliometric indices). To date, several dozen such indices have been proposed, the most significant of which was the so-called Hirsch index or h-index. Nevertheless, despite the incredibly significant advances in this specific area of sociology, the above problem is still far from resolved. In this regard, the key task of this Special Issue is to familiarize its readers with the latest achievements both in the search for new, more advanced bibliometric indicators and in the improvement of existing ones.