This comprehensive introduction to numerical mathematics consistently emphasizes practical applications. Additionally, it provides the reader with detailed guidance on numerical methods for solving ordinary and partial differential equations. Complemented by a chapter on modeling, the book aims to enhance students' understanding of the solution behavior of differential equations. Therefore, it is suitable both as a template for a multi-semester lecture series on numerical mathematics and for modeling lectures within one of the new degree programs in scientific computing. It is also well-suited for self-study and as a reference work.