What does a curve look like that completely fills the entire plane or space? Can a polyhedron be flexibly moved, even turned inside out? What is the projective plane or four-dimensional space? Are there soap bubbles that are not round spheres? How can we better understand the complicated structure of flows? In this book, you will experience mathematics from a visual perspective and discover fascinating and previously unseen images that provide illustrative answers to all these questions. Each image is accompanied by brief explanatory texts, numerous literature references, and plenty of web links. The book is for all friends of mathematics who do not want to see only dry text and endless formulas. From students to teachers, from undergraduates to professors, it aims to inspire and encourage everyone to engage with topics that may seem reserved for insiders.