This textbook is aimed at students of engineering and natural sciences and compiles all of higher mathematics as typically covered in undergraduate studies into a single volume. The starting point is always the question of what engineers and natural scientists encounter in their work, such as the modeling and optimization of technical processes or the description of physical laws. The work systematically explores the underlying mathematical topics, ranging from school mathematics through linear algebra to partial differential equations. New topics included in the thoroughly revised second edition are boundary value problems and tensor calculus. It features many exercises for further practice.