The book outlines the theory of complex signals. The reasons for the use of complex signals are explained and their main properties are given. Correlation properties of complex signals are studied in detail. Various frequency-modulated (with linear and quadratic FM, multi-frequency, etc.) and phase-manipulated (M-sequences, Legendre sequences, nonlinear, etc.) signals are considered. Solutions to the problems of synthesis of frequency-modulated and phase-manipulated signals by their autocorrelation functions and uncertainty bodiesSome issues of orthogonal signal systems construction are considered.