This book is the English translation of the textbook Numerische Mathematik, a highly successful European text on numerical analysis. It covers the usual classical topics of numerical analysis and also includes recent developments such as an up-to-date treatment of splines, linear optimization methods, and multidimensional numerical analysis. The text is desiged to be used in a first course in numerical analysis at the advanced undergraduate level or at the beginning graduate level. It features a careful balance between mathematical rigor and numerical insight and includes many worked out examples. Each section concludes with an extensive set of exercises that instructors should find useful in helping students to master the material. Moverer, the authors have also provided carefully researched historical notes that will be of particular interest to experts as well as students.