Qutubuddin Aibak built the Quwwatul Islam Mosque (his first major monument), Adhai Din Ka Jhonpra in Ajmer, and began construction of the Qutub Minar. However, he did NOT build the Jama Masjid - the famous Jama Masjid in Delhi was built by Shah Jahan much later in the 17th century, during the Mughal period.