This easy-to-follow guide provides students, teachers and industrial engineers with the necessary steps in discretizing continuous systems. It covers fundamental concepts in sampling and reconstruction of signal, and details the inspection method, the direct division method, the partial-fraction expansion method, the recurrence inversion method and the contour integration method. The book also introduces the transfer function and the stability condition of discrete-time systems in the closed loop. Indeed, it explains the global stability definition, the algebraic stability criterion and the stability in the frequency domain. The book also details the synthesis of digital controller for linear time invariant system and the use of a digital PID controller in practical speed control of a DC motor using an arduino card, to encourage readers to explore new applied areas of digital control.