This collective study focuses on a unique anonymous medieval document on ornamental geometry featuring geometrical constructions and textual instructions in Persian. Selections from the unpublished work of Alpay Ozdural (d. 2003) on this subject have been updated with original contributions by Jan P. Hogendijk, Elaheh Kheirandish, Gulru Necipoglu, and Wheeler M. Thackston. The chapters interpreting this fascinating document are followed, for the first time, by a facsimile, transcription, and translation, as well as drawings of incised construction lines invisible in the photographed facsimile.This publication intersects with the current interest in Islamic geometrical patterning as an inspiration for tessellation and parametrically derived forms in contemporary architecture and the arts. It aims to make this celebrated source more accessible, given its multifaceted relevance to historians of art, architecture, and science, as well as mathematicians, physicists, artists, and architects.For those who wish to obtain a copy of the full, unedited original book manuscript of Alpay Ozdural, where he discusses the mathematical properties of all geometrical constructions in the Anonymous Compendium as well as the step-by-step method for drawing each one, his work is available online at https://doi.org/10.6084/m9.figshare.5255416