The geometric patterns that cover the walls, ceilings and floors of the Alhambra in Granada, Spain have been the subject of study by many mathematical researchers ever since 1944, when E. Müller first reported the number of distinct planar crystallographic groups found there. In subsequent years, the count has varied, sometimes due to inconsistencies in the ways in which the patterns were chosen and analyzed. As such, contradictions and controversy still surround the issue. After a brief introduction, this paper will provide the criteria used by this author in an on-site visit in 2003 in order to catalog different crystallographic groups represented by patterns in the Alhambra. Each group identified is illustrated by a representative pattern.