Part I. One-Dimensional Variational Problems: 1. The classical theory
2. Geodesic curves
3. Saddle point constructions
4. The theory of Hamilton and Jacobi
5. Dynamic optimization
Part II. Multiple Integrals in the Calculus of Variations: 6. Lebesgue integration theory
7. Banach spaces
8. Lp and Sobolev spaces
9. The direct methods
10. Nonconvex functionals: relaxation
11. G-convergence
12. BV-functionals and G-convergence: the example of Modica and Mortola
Appendix A. The coarea formula
Appendix B. The distance function from smooth hypersurfaces
13. Bifurcation theory
14. The Palais¿Smale condition and unstable critical points of variational problems.
