The book is aimed at students of mathematics in teacher training programs at all school levels and in polyvalent bachelor's degree programs. It covers the fundamentals of arithmetic, elementary number theory, and algebra, as well as interesting extensions of these areas. This 6th edition has been completely revised and includes numerous comments and explanations on mathematical procedures, proof techniques, and notations in the introductory chapters on arithmetic and algebra. This further facilitates the transition to university mathematics for first-year students. The topic of complete induction has been newly included, and the subject of continued fractions has been extensively expanded. Approximately 400 exercises are provided to practice, deepen, and extend the material presented. Concise solution paths are available for all exercises.