Model Reduction of Parametrized Systems 1 Two ways to treat time in Reduced Basis Methods 2 Simultaneous empirical interpolation and reduced basis method. Application to non linear multi physics problem 3 A Certified Reduced Basis Approach for Parametrized Optimal Control Problems with Two sided Control Constraints 4 A reduced basis method with an exact solution certificate and spatio parameter adaptivity: application to linear elasticity 5 A Reduced Basis Method for Parameter Functions using Wavelet Approximations 6 Reduced basis isogeometric mortar approximations for eigenvalue problems in vibroacoustics 7 Reduced Basis Approximations for Maxwell’s Equations in Dispersive Media 8 Offline Error Bounds for the Reduced Basis Method 9 ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics 10 Reduced order semi implicit schemes for fluid structure interaction problems 11 True Error Control for the Localized Reduced Basis Method for Parabolic Problems 12 Automatic reduction of PDEs defined on domains with variable shape 13 Localized Reduced Basis Approximation of a Nonlinear Finite Volume Battery Model with Resolved Electrode Geometry 14 A posteriori error estimation of discrete POD models for PDE constrained optimal control 15 Hi POD solution of parametrized fluid dynamics problems: preliminary results 16 Adaptive sampling for nonlinear dimensionality reduction based on manifold learning 17 Cross Gramian Based Model Reduction: A Comparison 18 Truncated Gramians for Bilinear Systems and their Advantages in Model Order Reduction 19 Leveraging Sparsity and Compressive Sensing for Reduced Order Modeling 20 A HJB POD approach to the control of the level set equation 21 Model order reduction approaches for infinite horizon optimal control problems via the HJB equation 22 Interpolatory methods for H model reduction of multi input multi output systems 23 Model reduction of linear time varying systems with applications for moving loads 24 Interpolation Strategy for BT based Parametric MOR of Gas Pipeline Networks 25 Energy stable model order reduction for the Allen Cahn equation 26 MOR based Uncertainty Quantification in Transcranial Magnetic Stimulation 27 Model Order Reduction of Nonlinear Eddy Current Problems using Missing Point Estimation 28 On Efficient Approaches for Solving a Cake Filtration Model under Parameter Variation 29 Model reduction for coupled near well and reservoir models using multiple space time discretizations 30 Time dependent Parametric Model Order Reduction for Material Removal Simulations The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods proper orthogonal decomposition proper generalized decomposition approximation theory related to model reduction learning theory and compressed sensing stochastic and high dimensional problems system theoretic methods nonlinear model reduction reduction of coupled problems multiphysics optimization and optimal control state estimation and control reduced order models and domain decomposition methods Krylov subspace and interpolatory methods and applications to real industrial and complex problems. The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts guaranteeing a wide range of expertise and topics. Further it reflects an important effor t carried out over the last 12 years to build a growing research community in this field. Though not a textbook some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools master classes)