Optimality Criteria on Simple Regions -- Constraints, Lagrange Function, Optimality Criteria -- Parametric Aspects, Semi-Infinite Optimization -- Convex Functions, Duality, Separation Theorem -- Linear Inequalities, Constraint Qualifications -- Linear Programming: The Simplex Method -- The Ellipsoid Method -- The Method of Karmarkar for Linear Programming -- Order of Convergence, Steepest Descent, (Lagrange -)Newton -- Conjugate Direction, Variable Metric -- Penalty-, Barrier-, Multiplier-, Interior Point-Methods -- Search Methods without Derivatives -- One-Dimensional Minimization -- Graphs and Networks -- Flows in Networks -- Applications of the Max-Flow Min-Cut Theorem -- Integer Linear Programming -- Computability; the Turing machine -- Complexity theory -- Reducibility and NP-completeness -- Some NP-completeness results -- The Random Access Machine -- Complexity Theory over the Real Numbers -- Approximating NP-hard Problems -- Approximation Algorithms for TSP -- Approximation algorithms for Bin Packing -- A FPTAS for Knapsack -- Miscellaneous.