'Kernelization is one of the most important and most practical techniques coming from parameterized complexity. In parameterized complexity, kernelization is the technique of data reduction with a performance guarantee. From humble beginnings in the 1990's it has now blossomed into a deep and broad subject with important applications, and a well-developed theory. Time is right for a monograph on this subject. The authors are some of the leading lights in this area. This is an excellent and well-designed monograph, fully suitable for both graduate students and practitioners to bring them to the state of the art. The authors are to be congratulated for this fine book.' Rod Downey, Victoria University of Wellington 'Kernelization is an important technique in parameterized complexity theory, supplying in many cases efficient algorithms for preprocessing an input to a problem and transforming it to a smaller one. The book provides a comprehensive treatment of this active area, starting with the basic methods and covering the most recent developments. This is a beautiful manuscript written by four leading researchers in the area.' Noga Alon, Princeton University, New Jersey and Tel Aviv University 'This book will be of great interest to computer science students and researchers concerned with practical combinatorial optimization, offering the first comprehensive survey of the rapidly developing mathematical theory of pre-processing - a nearly universal algorithmic strategy when dealing with real-world datasets. Concrete open problems in the subject are nicely highlighted.' Michael Fellows, Universitetet i Bergen, Norway 'The study of kernelization is a relatively recent development in algorithm research. With mathematical rigor and giving the intuition behind the ideas, this book is an excellent and comprehensive introduction to this new field. It covers the entire spectrum of topics, from basic and advanced algorithmic techniques to lower bounds, and goes beyond these with meta-theorems and variations on the notion of kernelization. The book is suitable for students wanting to learn the field as well as experts, who would both benefit from the full coverage of topics.' Hans L. Bodlaender, Universiteit Utrecht 'The book is well written and provides a wealth of examples to illustrate concepts, while being succinct.' D. Papamichail, Choice 'The book does a good job in several ways: it can serve as the first textbook on this flourishing area of research; it is also very useful for self-study, as it contains quite a number of exercises, with further pointers to the literature. In addition, it gives quite a good overview of the present state-of-the-art and can therefore help researchers in the area to discover results that (s)he might have missed due to the speed in which the area has developed over the last decade.' Henning Fernau, MathSciNet 'This book studies the research area of kernelization, which consists of the techniques used for data reduction via pre-processing in order to speed up data analysis computations ... the book explores very novel and complex ideas, it is well written with attention to detail and easy to follow. The book concludes with a useful list of relevant references.' Efstratios Rappos, zbMATH 'The book manages to present an incredible number of techniques, methods, and examples in its 528 pages. Each chapter ends with a bibliographic notes section, which often provides some small historical context for the material covered. It also points to more current results and papers although it does so very briefly. Together, this makes the textbook a valuable resource book to researchers.' Tim Jackman and Steve Homer, SIGACT News