Certified Reduced Basis Methods for Parametrized Partial Differential Equations 1 Introduction and Motivation 2 Parametrized Differential Equations 3 Reduced Basis Methods 4 Certified Error Control 5 The Empirical Interpolation Method 6 Beyond the Basics 7 Appendix A Mathematical Preliminaries. This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time dependent problems non compliant and non coercive problems and applications with geometric variation are also discussed as examples.