This book, which is aimed at general readers interested in maths as well as professional mathematicians, addresses numerous aspects of this spell-binding science. In particular, the book shows how mathematics is structured and how it works. Practical examples are discussed as well as the general role of maths in culture and art, in nature and in everyday life. The topics covered range from forms of logical argumentation to numerical analysis, from simple applications in ancient civilisations to sophisticated tools in modern cultures, from natural shapes to artistic creations. Furthermore, it provides a comprehensible and comprehensive insight into the fascinating panorama of mathematics, emphasizing its importance in human history. It assumes only that readers have a grasp of the basic concepts of school maths, allowing them access to the exciting world of mathematics and to fall under its spell. Numerous examples and illustrations clarify the text. Rik Verhulst is Prof. emeritus in maths at the Karel de Grote University of Applied Sciences in Antwerp. He is the coordinator and co-author of several series of maths textbooks for secondary schools. He is well-known in professional circles for his numerous lectures at congresses and colloquia and for his contributions to various journals. As a collaborator and lecturer at the Belgian Centre for Methodology of Mathematics, the Vliebergh-Sencie courses, the Centre for Didactics of Mathematics at the Catholic University of Leuven and the Flemish Mathematical Olympiad, he has long been involved in the training of teachers and the preparation of pupils for the International Mathematical Olympiad.