To those who might think that using C*-algebras to study properties of approximation methods as unusual and even exotic, Hagen (mathematics, Freies Gymnasium Penig), Steffen Roch (Technical U. of Darmstadt), and Bernd Silbermann (mathematics, Technical U. Chemnitz) invite them to pay the money and read the book to discover the power of such techniques both for investigating very concrete discretization procedures and for establishing the theoretical foundation of numerical analysis. They speak both to students wanting to see applications of functional analysis and to learn numeral analysis, and to mathematicians and engineers interested in the theoretical aspects of numerical analysis.