The main intention of this book is to describe and develop the conceptual, structural, and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach, providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained, and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure; by itself as a first introduction to abstract mathematics; together with existing textbooks, to put their results into a more general perspective; or to gain a new and hopefully deeper perspective after having studied such textbooks.