The manual is a revised summary of lectures on one of the nine topics given at the Faculty of Physics of Novosibirsk State University as part of the course "Fundamentals of Functional Analysis" in the first half of the third semester . The theme of the Fourier Transformation is devoted to approximately 4 lectures and 3 seminars. The manual contains that part of the extensive Fourier transform theory, which, on the one hand, can be realistically set out and assimilated for the allotted curriculum period of time, and on the other hand, which is really necessary for students to master the physical courses read in the future.