One of the most common technology used then was - to fill mud around the building under construction and make a long ramp to transport material. Once they reach the top, the mud is removed layer by layer and finishing touch is given
Your vote on this answer has already been received
There are various stories being told about the reason the Qutub minar was built. Some say that it was constructed as tower of victory to declare the might of Islam. Some others have the view that it might have been used as a tower for defense.
The inscriptions at the base of the minaret tell that Firoz Shah Tughlak (AD 1351-88) added the last story in 1368. It is also believed that Sikandar Lodhi(AD 1489-1517) and Major R. Smith (1829) have undertaken several repair and restoration works on the tower. There are a numerous other Arabic inscriptions on the tower telling the history of Qutub.