The tutorial is dedicated to the 95 th anniversary of the birth of Professor N. Akhmetov. It contains well-known facts from the history of the theory of atomic structure, the fundamentals of this theory from the viewpoint of quantum mechanics as well as the periodic properties of chemical elements in their relation with the Periodic Law. The tutorial intended for the students studying in the educational program in the field “Chemical Technology”, the discipline “General and Inorganic Chemistry”, as well as for international students majoring in the framework of international educational programs, and for university graduates and teachers of chemistry. Prepared by the department of Inorganic Chemistry named after Professor N. S. Akhmetov.