In today’s deregulated environment, the nation’s electric power network is being forced to operate in a manner for which it was not intentionally designed. Therefore, system analysis is very important to predict and continually update the operating status of the network. This includes estimating the current power ﬂows and bus voltages (Power Flow Analysis and State Estimation), determining the stability limits of the system (Continuation Power Flow, Numerical Integration for Transient Stability, and Eigenvalue Analysis), and minimizing costs (Optimal Power Flow). This book provides an introductory study of the various computational methods that form the basis of many analytical studies in power systems and other engineering and science ﬁelds. This book provides the analytical background of the algorithms used in numerous commercial packages. By understanding the theory behind many of the algorithms, the reader/user can better use the software and make more informed decisions (i.e., choice of integration method and step-size in simulation packages).