Islamic ornaments are one of the greatest achievements of ancient geometers, artisans and craftsmen in the Middle East, Turkey, India, Spain, and North Africa. These ornaments are frequently used to decorate sacred, secular and private buildings, books, and furniture. Istanbul, in particular, is a place where such ornaments were, and still are, frequently used. In this book we will explore selected geometric ornaments from Istanbul. Many of these ornaments can be created by using very precise geometric constructions. We will analyze the structure of these ornaments and show how grids used to draw these ornaments, were constructed. A computer program, The Geometer's Sketchpad, will be used to construct these grids as well as complete ornaments. In a few examples a computer graphics program will be used to add some finishing touches to our work. Many of the examples presented in this book have a significant cognitive value. While creating them we can learn a number of important topics in geometry, e.g., constructions of regular polygons, constructions of figures circumscribed or inscribed in a circle, division of angles and segments into a given number of parts, transformations of figures, a touch of symmetry groups, and a number of other topics.