According to founding inscription, this building was built in 1250 by Fahrettin Ali, son of Grand Vizier Sahip Ata of Seljuks. It was built in the form of a large complex with mosque, tomb, imaret, inn and fountain; however only madrasa, masjid and tomb have survived to date. It is known that the structure was used as a hospital.
The Madrasa has a plan with an open courtyard and iwans. Courtyard is accessible from the southwest with a monumental gate. The rectangular courtyard is surrounded by riwaqs (posticoes), and the madrasa is located behind these porticoes.
Numerous bricks, rubble and different materials were used in the building. The winter rooms and the tomb section are covered with domes, while other room are covered with barrel vaults. The students' rooms are equipped with stove and cupboard niches and have one door and one window opening directly to the courtyard. There is a crypt under the tomb. At the bottom of the dome, there are remains of tile ornamented belt consists of interlaced geometric motifs looks like kufic script. Similarly, there is a tile panel in the middle of the dome. Also, there is a masjid built adjacent to the madrasah from the northern wall.
Stone Madrasa, which was used as the first museum building in Aksehir underwent extensive restoration between 1960-1965 and 1971. The building was used as an Archaeological Museum until 1986. Museum's collection consists several objects demonstrates an uninterrupted chronology from the Neolithic age to the end of the Ottoman period. In 2007, objects in the archaeology and etnography departments were moved to he newly opened Nasreddin Hoca Archaeology and Etnography Museum, but the large and heavy stone objects remained here. Today the museum collection also contains Turkish-Islamic period tombstones, chests, inscriptions and stone artefacts collected from Aksehir and its environs for historical integrity. There are also specially designed rooms to demonstrate daily life, education and stone masonry in the madrasa.
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