This three-volume book gathers peer-reviewed papers presented at the 21st International Conference on Geometry and Graphics (ICGG 2024), held in Kitakyushu, Japan, on August 5–9, 2024. The conference started in 1978 and is promoted by the International Society for Geometry and Graphics, which aims to foster international collaboration and stimulate the scientific research and teaching methodology in the fields of Geometry and Graphics. The ICGG 2024 covered the following five topics taken over from ICGG 2022: Theoretical Graphics and Geometry; Applied Geometry and Graphics; Engineering Computer Graphics; Graphics Education; Geometry and Graphics in History, to which a Related Topic section was added in response to the growing body of research on Geometry and Graphics. Volume 1 collects papers on three of these topics: Theoretical Graphics and Geometry, Graphics Education, and Related Topics. Given its breadth of coverage, the book introduces engineers, architects, and designers interested in computer applications, graphics, and geometry to the latest advances in the field, with a particular focus on science, the arts, and mathematics education.