"This book fills an important gap in the literature. It is an excellent starting point for young scholars approaching this new world, since it gives a well-balanced combination of theoretical aspects, practical details, and examples. ... It also gives a nice picture of the research in this field, particularly in the last two chapters which address advanced (yet crucial) topics." (Alessandro Veneziani, SIAM Review, Vol. 59 (1), 2016)

• 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.