1. Introduction -- 2. Review of direct methods for transient stability evaluations for systems with simplified models -- 3. Structure preserving energy functions for systems with nonlinear load models and generator flux decay -- 4. Structure preserving energy functions for systems with detailed generator and load models -- 5. Structure preserving energy functions for systems with HVDC and FACTS controllers -- 6. Detection of instability based on identification of critical cutsets -- 7. Sensitivity analysis for dynamic security and preventive control using damping controllers based on FACTS -- 8. Application of FACTS controllers for emergency contron : I -- 9. Application of FACTS controllers for emergency control : II.