The book offers a clear and careful introduction to advanced mathematics with a well-thought-out didactic structure, where nearly all concepts are derived and justified from previously covered content. The hierarchical organization supports interconnected learning, which is essential for a secure and long-term mastery of the material. Volume 1 covers linear algebra as well as differential and integral calculus of a single variable, including some numerical topics. The many professionally designed graphics contribute to understanding, as do the fully worked-out examples. It is a valuable companion for all students in engineering and natural science programs. For students in mathematics programs, especially those in teacher training, the book can serve as an illustrative introduction to differential and integral calculus.