The book offers a new compilation of material that connects fundamental topics from algebra and number theory, designed for use in bachelor's programs and modular teacher training courses. It introduces the abstract concepts of algebra in constant contact with concrete problems from elementary number theory, with an eye toward applications, and provides insights into advanced topics. In both areas, a level is reached that equips non-specialists with the necessary tools for most applications, while also encouraging a deeper engagement with algebra and number theory, serving as a solid foundation for further study. For the third edition, in addition to a general revision and error correction, numerous examples and exercises have been added.