Textbook in PDF format This book focuses on the partial spectral discretization (PSD)-based eigenvalue computation methods for large-scale time-delay systems. Due to past-dependence in the evolution of a system, time delays may greatly affect the system’s dynamics. For example, wide-area damping controllers in the interconnected power systems are fed by remote synchrophasor measurements and thus inevitably introduce time delays into the control loop. These delays ranging from tens to hundreds of milliseconds can deteriorate the performance of the controllers and further jeopardize the power system stability. Therefore, this book addresses two classes of efficient eigenvalue computation methods for time-delay systems based on the PSD idea, as well as their applications to power systems with inclusion of time delays. The methods are expected to obtain the accurate stability boundary of time-delay systems with affordable computational burden