The power grid can be considered one of twentieth-century engineering's greatest achievements and, as grids and populations grow, robustness is a factor that planners must take into account. Since the underlying physics is mathematically complex, and modeling is complicated by lack of accurate data, power grid robustness is a complex problem. This book sheds light on this problem by introducing the engineering details of power grid operations from the basic to the detailed; describing how to use optimization and stochastic modeling, with special focus on the modeling of cascading failures and robustness; providing numerical examples that show 'how things work'; and detailing the application of a number of optimization theories to power grids. As a result, it will be useful to both operations researchers wishing to learn about power grids, as well as power engineers seeking an in-depth understanding of optimization methodologies and the rigorous thinking used in optimization.