From the reviews: “This book by Panayot Vassilevski is the first comprehensive text in the literature on multilevel preconditioners in the formulation of approximate block factorizations. … The presentation is comprehensive and detailed, and the theory is illustrated by classical examples of block factorizations like the block-ILU factorization. … valuable addition to the collection of research books for any ... Read moreresearcher working in the field of multilevel methods who is interested in getting a different view on methods he or she knows and has helped to develop and shape.” (Martin J. Gander, Mathematical Reviews, Issue 2010 b) “This well-written and timely book fills a great need in the literature. It provides a thorough and yet readable treatment of cotemporary theory … . book will be readily accessible to graduate students past introductory analysis and linear algebra. … The book will be a important reference for anyone interested in practical or theoretical aspects of iterative solvers for finite elements, from students to established researchers. Early chapters could serve well as a textbook on the topic.” (Jan Mandel, Zentralblatt MATH, Vol. 1170, 2009) “The presentation sets out with a tutorial on finite elements, where already properties of matrices which turn out essential later on are exhibited. … this presentation will be of major interest to researchers and advanced students in that field.” (H. Muthsam, Monatshefte für Mathematik, Vol. 157 (1), May, 2009) Show Less