Ala al Din Khalji's (reg. 1296 - 1316) madrasa is located in the southwestern part of the Qutb complex. It can be seen beyond Iltutmish's qibla wall addition to the Qutb mosque. The L-shaped madrasa consists of the college, organized around a quadrangular court, with Khalji's own tomb on the southern corner.
At present, the tomb structure itself is in ruins, and reconstructions are purely conjectural. It is known that Khalji's tomb has two smaller chambers on the eastern and western sides, connected by a narrow passageway; recent excavations have unearthed graves within them. The walls of these chambers supported domes on an octagonal base with pendentives assisting in the transition. The three buildings (the tomb itself and the two smaller chambers) are contained within a common enclosure wall with a clear passage around it for circumambulation.
The L-shaped madrasa is a series of individual cell-like apartments used for religious teaching. They run along two edges of a courtyard that measures approximately 35 by 25 meters. The rooms of the madrasas are roofed in a manner similar to that of Khlaji's tomb: corbelled pendentives achieve the transition from the walls to an octagonal ring that supports the dome.
Sources:
Balasubramaniam, R. 2005. The World Heritage Complex of the Qutub, New Delhi: Aryan Books International, 104-106.
Nath, R. 1978. History of Sultanate Architecture; New Delhi: Abhinav Publications, India, 46.
Page, J.A. 1970. An Historical Memoir on the Qutb: Delhi, New Delhi: Laxmi Book Store, 17, 18.