This book consists of two parts: theoretical and practical. The theoretical part includes information on Fourier transform, filters and signal decomposition. The general theory of wavelets is outlined in sufficient detail, including wavelets with an arbitrary natural scaling factor and multidimensional wavelets with a matrix scaling factor, harmonic wavelets and multi-wavelets. In the second, practical part of the book, the chapter on the capabilities of Wavelet Toolbox MATLAB R2018b has been significantly updated, which now includes decompositions into empirical EMD modes, procedures for machine and deep learning, two-dimensional continuous wavelet transformation and many other interesting new procedures.