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The use of fractional order operators presents an alternative for the development of control strategies applied to industrial processes that allow for greater robustness and stability in the presence of perturbations and uncertainties that affect the real system. This book presents an introduction to the fundamentals of fractional order control, starting with the definition of the fractional order derived operator and its application to control theory covering the concepts of transfer function, stability analysis and frequency domain response. In addition, the structure for the fractional order PID controller (FOPID) and a methodology for its tuning applied to a first order system with delay are defined. Finally, a discrete time representation of the FOPID controller is presented for its practical implementation in industrial process control.