I Theoretical and Practical Concepts of Modeling Languages -- 1 Mathematical Optimization and the Role of Modeling Languages -- 2 Models and the History of Modeling -- 3 Mathematical Model Building -- 4 Theoretical Concepts and Design of Modeling Languages -- 5 The Importance of Modeling Languages for Solving Real-World Problems -- II The Modeling Languages in Detail -- 6 The Modeling Language AIMMS -- 7 Design Principles and New Developments in the AMPL Modeling Language -- 8 General Algebraic Modeling System (GAMS) -- 9 The LINGO Algebraic Modeling Language -- 10 The LPL Modeling Language -- 11 The MINOPT Modeling Language -- 12 Mosel: A Modular Environment for Modeling and Solving Optimization Problems -- 13 The MPL Modeling System -- 14 The Optimization Systems MPSX and OSL -- 15 The NOP-2 Modeling Language -- 16 The OMNI Modeling System -- 17 The OPL Studio Modeling System -- 18 PCOMP: A Modeling Language for Nonlinear Programs with Automatic Differentiation -- 19 The Tomlab Optimization Environment -- III The Future of Modeling Systems -- 20 The Future of Modeling Languages and Modeling Systems -- References

1. Mathematics
2. Programming languages (Electronic computers)
3. Numerical analysis
4. Computer science -- Mathematics
5. Mathematical models
6. Mathematical optimization
7. Mathematics
8. Mathematical Modeling and Industrial Mathematics
9. Optimization
10. Symbolic and Algebraic Manipulation
11. Numeric Computing
12. Programming Languages
13. Compilers
14. Interpreters