The subject of this textbook is the process of applying mathematics. The focus is on the concept of functions and mathematical methods for modeling functional dependencies between two quantities. The book is characterized by the following special features: real data as the basis for many models, which is an important prerequisite for authentic and credible teaching at the university and school levels. The use of technology as a tool for problem-solving and illustrating concepts and relationships. The interconnection of various areas of mathematics such as elementary function theory, analysis, statistics, linear algebra, and numerical methods. Detailed derivations of results, as well as exercises and questions at the end of each chapter with partially worked-out solutions and hints for solutions, aid in deepening the material.