This book aims to provide students with an introduction to numerical mathematics. It is based on a concept that has been carefully refined by the author over many semesters at the University of Hamburg and takes into account the specificities of the subject with numerous examples and exercises, establishing a connection to programming. Students will learn to independently work through and deepen their understanding of the material. The text develops an awareness of possible reductions in the effort required by an algorithm, the necessary stability that sets limits on the ever-present rounding errors, and existing but yet unused parallelizations that help save computation time. In this 5th edition, two new sections on wavelets and radial basis functions have been added. A proven textbook with numerous illustrations, examples, and programs.