This book, dedicated to the 100th anniversary of the law of periodicity, gives a comprehensive analysis of the process of discovery by D. I. Mendeleev of the periodic law and the development of the periodic system of elements. The problem of prediction and discovery of new elements in connection with the law of periodicity is considered. This problem has now become extremely relevant due to the staging of research on the synthesis and detection in nature of superheavy transuranic elements. In this regard, the issue of the content of the concepts "criterion of the reliability of synthesis" and "criterion of the reliability of discovery" was discussed.