1 Introduction -- 1.1 Introduction -- 1.2 Formalisation of a model reduction problem -- 1.3 The importance of model order reduction -- 1.4 Notations and mathematical backgrounds -- References -- 2 Model Reduction -- 2.1 Overview of common model order reduction methods -- 2.2 Frequency domain methods for model order reduction -- 2.3 Time domain methods for model order reduction -- 2.4 Balanced realisation-based model order reduction -- 2.5 Balancing approaches for symmetrical systems -- 2.6 "Hankel"-based methods -- 2.7 Model order reduction examples -- References -- 3 Guidelines for Obtaining Low Order Models -- 3.1 Introduction -- 3.2 Reasons for using an expert system -- 3.3 Approaches for dealing with uncertainty -- 3.4 A suitable software environment for EXPRED -- 3.5 Expertise organisation -- 3.6 Consultation of the expert system -- 3.7 Quantitative assessment of reduced model performance -- References -- 4 Applications in Electrical Engineering -- 4.1 Introduction -- 4.2 Power system model order reduction -- 4.3 Model order reduction in transient electromagnetic phenomena -- 4.4 Approximated model identification of electrical induction machines -- 4.5 The approximated flywheel generator converter model in the JET (Joint European Torus) load -- 4.6 The Kokotovic reduced-order regulator problem -- 4.7 Techniques for characterising electrical network properties and model order reduction -- References -- 5 Advanced Topics in Model Reduction -- 5.1 Reduced-order models of high-order systems with bounded parameters -- 5.2 High-order systems with low-order compensators -- 5.3 Multidimensional system approximation -- 5.4 Balancing techniques for very large scale systems -- 5.5 Model order reduction for linear time-varying systems and non-linear systems -- 5.6 Towards unified software support for model order reduction -- 5.7 New software tools for model order reduction -- 5.8 Concluding remarks -- References -- Appendix A EXPRED Decision Tree -- Appendix B MATLAB Program Codes of the Main Reduction Algorithms.