The concept of discrete time axis, the concept of signals with discrete time and operations with signals with discrete time. Fundamental aspects of the signal theory with discrete time in the arbitrary field. Operations with signals with discrete time in the field of real numbers. Bilateral Z-transformation, Unilateral Z-transformation, Discrete Fourier transformation. Fundamental aspects of the discrete system theory, description of the terminal behavior of the discrete system elements, their classification and connection. Linear time invariant discrete systems: analysis in the time domain and stability. Analysis of the linear time invariant discrete systems using unilateral Z-transformations and discrete Fourier transformations. The concepts of filtering, introduction to classification and synthesis of digital filters. Hardware implementation of discrete systems.