On September 16, the Institute seminar on “Representation of Ridge functions and many group of variables in the form of the sum of Ridge functions” was held. The head of “Functions theory” department doctor of mathematical sciences Vugar Ismayilov gave a talk. In the report he spoke about the role of the Ridge functions in the contemporary mathematical science and informed the participants about the monograph “A. Pinkus, Ridge functions, published in Cambridge University press, 2015” . In the report he also analyzed the representation of functions of many group of variables by the Ridge functions and discussed necessary and sufficient conditions for these representations.