Anyone who visits the Alhambra palace in Granada will marvel at the intricate arabesque designs that decorate everything from the tiles and plasterwork to woodcarvings and the lattice-work in the windows. These designs from Islamic art are not only beautiful to look at but also rich in symmetry, involving the repetition of a fundamental motif or element in an ordered and mathematically perfect way. Indeed, the way in which these motifs are repeated illustrate the basic rules of reflection, rotation, translation and “glide reflection” – a reflection followed by a translation parallel to the axis of reflection. This video, which introduces the mathematics of symmetry and its application to crystallography, gives examples of the many arabesque designs at the Alhambra. Amazingly, it turns out that all 17 planar-crystallographic “groups” appear as symmetry groups in the arabesque designs at the palace. The film is easy to follow and will be useful for those who have to teach crystallography.