1. Mathematical preliminaries 2. Optimization in Rn 3. Existence of solutions: the Weierstrass theorem 4. Unconstrained optima 5. Equality constraints and the theorem of Lagrange 6. Inequality constraints and the theorem of Kuhn and Tucker 7. Convex structures in optimization theory 8. Quasi-convexity and optimization 9. Parametric continuity: the maximum theorem 10. Supermodularity and parametric monotonicity 11. Finite-horizon dynamic programming 12. Stationary discounted dynamic programming Appendix A: Set theory and logic: an introduction Appendix B: The real line Appendix C: Structures on vector spaces Bibliography.