Numerical mathematics is one of the cornerstones of the study of mathematics, engineering, physics and computer science. This two-volume textbook is designed for introductory lectures and lays a solid foundation for further learning units. The text is based on lecture manuscripts that the author has been using for about 30 years for his basic lectures in the field of numerical mathematics and scientific computing at the Friedrich Schiller University Jena. The book covers the entire field of numerical mathematics from classical techniques such as the Gaussian algorithm and Newton's method to modern algorithms such as cubic spline interpolation, least-squares approximation using Householder and Givens transformations and deflation techniques. The methods are described with mathematical precision, implemented in MATLAB codes and demonstrated using examples. The MATLAB codes are available for download on the publisher's website so that readers can carry out their own experiments with the numerical methods. Thanks to its didactic structure and the numerous illustrative examples and exercises, this book is ideal for reading alongside lectures and as a basis for successful self-study. At the same time, it can be used by mathematicians, scientists and engineers as a profound reference work.