Girih (Persian: گره, "knot", also written gereh) are decorative Islamic geometric patterns used in architecture and handicraft objects, consisting of angled lines that form an interlaced strapwork pattern.

Girih decoration is believed to have been inspired by Syrian Roman knotwork patterns from the second century. However, its mathematical patterns, structured around multiple lines of symmetry, are based on innovations in mathematics that occurred in the Islamic world after the ninth century. The earliest girih dates from around 1000 CE, and the artform flourished until the 15th century. Girih patterns can be created in a variety of ways, including the traditional straightedge and compass construction; the construction of a grid of polygons; and the use of a set of girih tiles with lines drawn on them: the lines form the pattern. Patterns may be elaborated by the use of two levels of design, as at the 1453 Darb-e Imam shrine. Square repeating units of known patterns can be copied as templates, and historic pattern books may have been intended for use in this way.

The 15th century Topkapı Scroll explicitly shows girih patterns together with the tilings used to create them. A set of tiles consisting of a dart and a kite shape can be used to create aperiodic Penrose tilings, though there is no evidence that such a set was used in medieval times. Girih patterns have been used to decorate varied materials including stone screens, as at Fatehpur Sikri; plasterwork, as at mosques and madrasas such as the Hunat Hatun Complex in Kayseri; metal, as at Mosque-Madrassa of Sultan Hassan in Cairo; and in wood, as at the Mosque–Cathedral of Córdoba.

The girih style of ornamentation is thought to have been inspired by 2nd century AD Syrian Roman knotwork patterns. Its mathematical patterns, structured around multiple lines of symmetry, are based on innovations in mathematics that occurred in the Islamic world after the ninth century. These had curvilinear interlaced strapwork with three-fold rotational symmetry. The Umayyad Mosque (709–715) in Damascus, Syria has window screens made of interlacing undulating strapwork in the form of six-pointed stars. Early examples of Islamic geometric patterns made of straight strap lines can be seen in the architecture of the surviving gateway of the Ribat-i Malik caravanserai, Uzbekistan, built in 1078. The wide application of girih in architecture reflects the close relationship between Islamic architecture, geometry, and craft. Architecture was classified in the field of practical geometry in the early Islamic period, and building projects always involve a muhandis (geometer).

The earliest form of girih on a book is seen in the frontispiece of a Quran manuscript from the year 1000, found in Baghdad. It is illuminated with interlacing octagons and thuluth calligraphy.

In woodwork, one of the earliest surviving examples of Islamic geometric art is the 13th-century minbar (pulpit) of the Mosque of Ibn Tulun, Cairo. Girih patterns can be created in woodwork in two different ways. In one, a wooden grille with polygons and stars is created; the holes can be left as they are, or filled with some material. In the other, called gereh-chini small wooden panels of geometric shapes are created individually, and combined to create an elaborate design.

In 10th century a systematic investigation of geometric patterns was conducted by Persian mathematician and astronomer Abu al-Wafa' Buzjani in the House of Wisdom. In his treatise A Book on Those Geometric Constructions Which Are Necessary for a Craftsman, he explained the geometric structure and illustrates the methods of drawing polygons within other shapes (mostly circles) for craftsmen and artisans. This book laid the groundwork for designing girih by explaining fundamental grammar for construction girih patterns.

The term "girih" was used in Turkish for polygonal strap patterns in architecture as early as the late 15th century. In the same period, artisans compiled girih pattern books such as the Topkapı Scroll.