1. Convex Cones and linear Inequalities -- 1. Separation theorems -- 2. Cones and duals -- 3. Linear inequalities over cones -- 4. Theorems of the alternative -- 2. Mathematical Programming over Cones -- 5. Linear programming -- 6. Quadratic programming -- 7. The complementarity problem -- 8. Non-linear programming -- 3. Cones in Matrix Theory -- 9. Cones of matrices -- 10. Lyapunov type theorems -- 11. Cone monotonicity -- 12. Iterative methods for linear systems -- References -- Glossary of Notations.