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This book is to present learning material for students, instructors, engineers in the field of power system transient stability who wish to learn the design of the controller unit of FACTS devices and to choose a suitable method for seeking their optimal placement in order to improve the transient stability. The book begins with the general background of power network blackout events around the globe. The methodology of rotor angle stability is recalled for the sake of analyzing the transient stability. The method based on the controllability and observability Gramian is developed for seeking an optimal placement of FACTS devices in the power system in order to dampen the electromechanical oscillations. In addition, the control strategy for each FACTS device is also proposed. Three FACTS devices namely, SVC, STATCOM, and TCSC, the power systems as IEEE-39bus, IEEE-24bus, and Vietnam power system, and the softwares as PSS/E, EMTP-RV, and MATLAB are carried out to perform this research. The book is a monographic material for the Research Students and Academicians in the field of power system stability.