In a book the basic varieties of adaptive filters and their application are examined in the radiotechnical systems and communication networks. An idea is given about the mathematical objects and methods, used in the theory of adaptive filtration of signals. The receptions of receipt of calculable procedures, procedures and properties of such algorithms of adaptive filtration, as algorithms of Newton and наискорейшего lowering, are examined, algorithms on to the criterion of leastsquare, recursive algorithms on the criterion of leastsquares and their rapid (calculable effective) versions| recursive algorithms on the criterion of leastsquares for multichannel filters and their version for treatment of non-stationary signals, and also multichannel algorithms of affine projections. Description of standard and non-standard applications is Given for the design of adaptive filters on modern programming of MATLAB languages, LabVIEW and SystemVue, and also realization of adaptive filters on the modern digital alarm processors of home and foreign production.The feature of book is expositions of theoretical materials for the most general case - adaptive filters with complex gravimetric coefficients, presence of divisions on multichannel adaptive filters and algorithms of adaptive filtration non-stationary signals.A book is the first systematic exposition of theory to adaptive filtration in Russian language.She is intended for research workers, engineers, graduate students and students of radiotechnical and coherent specialities, studying and using digital treatment of signals and, in particular, adaptive filtration of signals in practice.