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. Power grid robustness is a complex problem for two reasons: the underlying physics is mathematically complex, and modeling is complicated by lack of accurate data. This book sheds light on this complex 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.?????