The course deals with the Fourier transform of functions of several variables and its use in diffraction theory and in structure analysis. The introductory parts are focused on the definition of the Fourier transform, spatial frequencies, spectrum of spatial frequencies, and on the relevance of the Fourier transform to the diffraction theory. Then, the properties of the Fourier transform are presented via mathematical theorems and are illustrated by the Fraunhofer diffraction patterns. In this way a view of the general properties of the diffraction phenomena of this type is obtained. At the end the kinematical theory of diffraction by crystals is presented as an application of the Fourier transform of three-dimensional lattices.