No matter how great the contribution to the creation of classical science by such giants as N. Copernicus, J. Kepler, Tycho Brahe and others, it is Galileo who is considered to be its main founder and hero. Of course, Galileo was responsible for a number of important scientific achievements, but he not only laid the foundations of classical physics, he did something more - he created a new type of scientific thinking. He believed in the possibility of mathematical comprehension of the physical world. His element is thought experiments and real experiments. The main experiment of the “Dialogue” was an experiment to restructure human thinking. The works of Galileo - and above all the "Dialogue" - are a living testimony of the era, "genuine records of thought" (B. L. Pasternak) on its difficult transition from the world of Aristotle and St. Thomas to the world of Copernicus and Galileo. This publication is accompanied by an introductory note specially written for it article d.x. n., director of the D. I. Mendeleev Museum-Archive of St. Petersburg State University Igor Sergeevich Dmitriev, talking about the main ideas and history of the publication of “Dialogue” and the dramatic events that followed it, the analysis of which seems very relevant today.