In the chapter, Discrete-time Systems, system classification, system response, system stability and realization of systems are presented. The discretization of continuous systems into discrete-time systems if first presented. Computation of the response of discrete-time systems by iteration, solving the difference equation and by convolution are described with appropriate examples. Then, systems are classified in terms of linearity, time-invariance, causality, stability, instantaneous or dynamic response and inversibility. The classification helps to choose appropriate tools for their analysis. The response of systems to complex exponential signal is described, which is important in finding the steady-state response. The system stability is analyzed in terms of its impulse response. The basic components used to build discrete systems are presented with an example of realization. Decomposition of large systems into smaller systems connected in cascade and parallel is then presented. Systems with feedback are introduced.