The book is based on lectures that have been given for a number of years to students of mathematical specialties of the Faculty of Mathematics and Mechanics of Leningrad University .. From the available textbooks of quantum mechanics, the book differs in that it is focused mainly on the mathematical audience. In this regard, more attention is paid to the general issues of quantum mechanics and its mathematical apparatus. In a different way than is customary in the physical literature, the basics of quantum mechanics are presented, the relationship between quantum and classical mechanics is described in detail, paragraphs devoted to the application of group representation theory and mathematical questions of quantum scattering theory are included. In addition to students of mathematics, the book can also be useful to students specializing in theoretical physics, which it will allow them to look at quantum mechanics from a new point of view for them.