Abdur Rahim Khan (d. 1626) was the son of Bairam Khan, the protector of Akbar during his minority, and himself served Jahangir for many years. He is a noted architectural patron, among whose works are several important civic institutions in Burhanpur. His tomb is is situated near Humayun's Tomb just outside of the Nizam ud Din Auliya Shrine Complex. Its form is derived from the Tomb of Humayun, employing a compact version of the 'cube' type tomb much used in Delhi. The plinth upon which it rests serves as a garden, with water channels and pools, replacing the spacious tomb garden as seen in Humayun's Tomb. 

It is a large domed structure, square in plan, faced with red sandstone and white marble trim. The plan is considered part of the experimentation that led to the development of the Taj Mahal scheme. The mausoleum building is faced in stone, and is topped with a marble dome. The tomb was stripped of its facing in the 18th century, for use in the tomb of Safdar Jang. It once stood in a quartered garden, which has since disappeared. The Tomb is at present in poor condition.

The structure fell into a state of disrepair and was restored by the Aga Khan Trust for Culture between 2014-2020. 

Sources:

Tillotson, G.H.R. 1990. Mughal India. San Francisco: Chronicle Books, 50.

Asher, Catherine. 1992. The New Cambridge History of India: Architecture of Mughal India. Cambridge University Press, 142-3.