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. Language: English