Short answers, pulled from the story.
The Taj Mahal was commissioned in 1631 by the fifth Mughal emperor, Shah Jahan, as a mausoleum for his wife Mumtaz Mahal, who died on the 17th of June 1631 while giving birth to their fourteenth child, Gauhara Begum. Shah Jahan's grief was documented by contemporary historians, who recorded that he withdrew from royal affairs for a week and abandoned music and lavish dress for two years after her death.
The Taj Mahal was designed and built under the leadership of Ustad Ahmad Lahori, Shah Jahan's court architect, with a multinational team that included Ottoman dome designer Ismail Afandi, Persian architects Ustad Isa and Isa Muhammad Effendi, calligrapher Amanat Khan Shirazi, and specialist craftsmen from Bukhara, Syria, Persia, Baluchistan, and southern India. More than 20,000 workers and artisans were involved in its construction.
The mausoleum itself was completed in 1648, but construction on the surrounding complex continued until 1653, when the entire project was finished. The first ceremony held at the site took place on the 6th of February 1643, when Shah Jahan observed the 12th anniversary of Mumtaz Mahal's death.
The cost of the Taj Mahal complex was estimated at the time to be around 32 million. A 2015 calculation placed the equivalent value at approximately 52.8 billion.
The mausoleum is veneered in white marble from Makrana in Rajasthan, inlaid with 28 types of precious and semi-precious stones sourced from across the world, including jade from China, turquoise from Tibet, lapis lazuli from Afghanistan, sapphire from Sri Lanka, and carnelian from Arabia. Other buildings in the complex were built with red sandstone quarried from Fatehpur Sikri in Uttar Pradesh.
The Black Taj Mahal myth holds that Shah Jahan planned to build a second mausoleum in black marble across the Yamuna river. The story originates from writings of the European gem merchant Jean-Baptiste Tavernier, who visited Agra in 1665. Excavations in the 1990s disproved the idea; apparent black marble ruins in the Mehtab Bagh were found to be discolored white stones, and in 2006 archaeologists demonstrated that the dark image seen across the river was simply the Taj Mahal's own reflection in the pool.