The first chapters of this book deal with Haar bases, Faber bases and some spline bases for function spaces in Euclidean \(n\)space and \(n\)cubes. These are used in the subsequent chapters to study sampling and numerical integration preferably in spaces with dominating mixed smoothness. The subject of the last chapter is the symbiotic relationship between numerical integration and discrepancy, measuring the deviation of sets of points from uniformity. This book is addressed to graduate students and mathematicians who have a working knowledge of basic elements of function spaces and approximation theory and who are interested in the subtle interplay between function spaces, complexity theory and number theory (discrepancy). A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in complexity theory and number theory. Table of Contents  Function spaces
 Haar bases
 Faber bases
 Sampling
 Numerical integration
 Discrepancy
 Bibliography
 List of Figures
 Symbols
 Index
