The book provides an overview of curves with loops and peaks, spirals and rosettes, ellipses, and other conic sections, which are among the most fascinating objects in mathematics. Construct and explore these with GeoGebra and other mathematical tools or by hand, and creatively generate additional curves. The necessary mathematical tools are carefully developed and applied in various contexts through derivations, proofs, and references. The goal of the book is to offer a contemporary comprehensive presentation that aims to provide new impulses for teacher training. Mathematical competencies that are truly relevant in schools should be developed around this "forgotten" topic. However, students, teachers, and learners from grade 8 to old age should also find joy in engaging in as independent mathematical activities as possible.