There is much to see and admire in the Alhambra Palace: its exquisite rooms, decorated with stone and wood carvings, finest ornaments, and calligraphy; night sky represented in ceilings built of thousands of pieces of wood; gardens, courtyards and fountains; monuments, towers, archways - the list is endless. Quite possibly, an immense wealth of ornamental patterns, friezes, mosaics, star designs, and brickwork motifs tops the list. Among those, mosaics are perhaps the most interesting and the most intriguing. Scientists and artists working in the Islamic world pushed geometry to its limits, creating patterns and configurations whose sophistication has never been surpassed. Investigating numerous possibilities, based on experience and long tradition, builders of mosaics in the Alhambra created them all - in the sense of the mathematics theorem on the classification of plane crystallographic groups (or wallpaper patterns). Mosaics are an invitation for a 'dynamic' experience, different from enjoying a picture of a landscape. Our eye is not able to focus on one location; there is no centre, no boundary and no preferred direction. This paper suggests the use of a vocabulary from geometry to express some of our visual experiences related to mosaics.