The book addresses the theory of signals and (linear) systems as well as their applications. After an introduction using examples from various application areas, the fundamental techniques for describing continuous-time linear time-invariant systems and their effects on signals are discussed. The transition to digital signal processing is prepared through the derivation and discussion of the sampling theorem. Subsequently, the methods of system theory for digital signal processing are presented. A focus is placed on the discussion of the discrete Fourier transform. In particular, the relationships between DFT/FFT spectra and the spectra of continuous-time signals are emphasized. The methods covered are applied to the processing of stochastic signals, making them usable for practical applications.