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1. Introduction and overview
2. System modeling and stability problems
3. Lyapunov stability and stability regions of nonlinear dynamical systems
4. Quasi-stability regions : analysis and characterization
5. Energy function theory and direct methods
6. Constructing analytical energy functions for transient stability models
7. Construction of numerical energy functions for Lossy transient stability models
8. Direct methods for stability analysis : an introduction
9. Foundation of the closest UEP method
10. Foundations of the potential energy boundary surface method
11. Controlling UEP method : theory
12. Controlling UEP method : computations
13. Foundations of controlling UEP methods for network-preserving transient stability models
14. Network-reduction BCU method and its theoretical foundation
15. Numerical network-reduction BCU method
16. Network-preserving BCU method and its theoretical foundation
17. Numerical network-preserving BCU method
18. Numerical studies of BCU methods from stability boundary perspectives
19. Study of the transversality conditions of the BCU method
20. The BCU-exit point method
21. Group properties of contingencies in power systems
22. Group-based BCU-exit method
23. Group-based BCU-CUEP methods
24. Group-based BCU method
25. Perspectives and future directions.

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