The book is about symmetric geometric patterns of Islamic art. It has educational, aesthetic, cultural and practical purposes. The central purpose of the book is to bring to the attention of the world in general and the people of the Islamic countries in particular, the potential of this art in the context of mathematical education. This book sets out to place the study of Islamic patterns within the wider framework of symmetry. The symmetry structure of about 250 Islamic patterns is presented. Simple algorithms suitable for modern computer graphics are given for the construction of two-dimensional periodic patterns. This book should be suitable for both the lay reader keen to explore Islamic art and the specialized mathematician.