The Taj Mahal was built by Shah Jahan. Option 1, Jahangir, is incorrect because he was the fourth Mughal emperor and ruled from 1605 to 1627, while the construction of the Taj Mahal began in 1632. Option 3, Sher Shah, is also incorrect as he was the founder of the Sur Empire in North India and ruled from 1540 to 1545, which was much earlier than the construction of the Taj Mahal. Option 4, Nadir Shah, is incorrect as well because he was a Persian military leader who invaded India in the 18th century, long after the construction of the Taj Mahal. Therefore, the only correct option is option 2, Shah Jahan, who ruled from 1628 to 1658 and commissioned the construction of the Taj Mahal as a mausoleum for his beloved wife, Mumtaz Mahal.