The book "Subdivision Surfaces" provides a comprehensive summary of the current state of knowledge regarding subdivision algorithms, which have gained significance in computer graphics and engineering applications since their introduction in 1974. It covers both classical results and the latest unpublished materials, including a new framework for constructing C^2 algorithms. The focus is on developing a thorough mathematical theory that enables readers to understand the fascinating properties of subdivision. The book is aimed at researchers, engineers, academic educators, and students interested in the fundamentals of this emerging discipline of applied geometry.