Science and art are essential components of human culture that originally developed independently of each other. However, over time, connections and mutual influences have increasingly emerged, with geometric figures serving as an important bridge for the relationships between mathematics and art. What can mathematics contribute to art, specifically in ornamentation? Mathematics explores concrete and abstract, finite and infinite structures. Ornaments are structured by their largely symmetrical design. The aim of this book is to elucidate such relationships from the perspective of geometry and group theory. We have structured our discussions in a way that allows readers to follow them using their school knowledge, addressing two different groups of readers.