The Taj Mahal is not a palace.
It is in fact a white marble mausoleum, a symbol of eternal love, built by the the Mughal emperor, Shah Jahan, to house the tomb of his favourite (third) wife, Mumtaz Mahal, who had borne him 13 children, ultimately dying in childbirth to the 14th.
The mausoleum also houses the tomb of Shah Jahan himself, the only non-symmetrical part of the entire complex, for this was only ever designed as the tomb for one person, his love.
Interesting fact: it took over 20,000 workers, comprising artisans, craftsmen, laborers, calligraphers, stone-cutters, painters and other craftsmen under the guidance of the court architect to build the complex.