Short answers, pulled from the story.
Sawai Jai Singh II (the 3rd of November 1688 - the 21st of September 1743) was the 30th Kachwaha ruler of the Kingdom of Amber. He is known for founding the planned city of Jaipur, building the Jantar Mantar astronomical observatories across India, and being considered the most enlightened king of eighteenth-century India.
Sawai means one and a quarter times superior to his contemporaries. The title was given to Jai Singh by Mughal Emperor Aurangzeb following his performance at the siege of Khelna Fort in the Deccan in 1702.
Construction of Jaipur began as early as 1725, with the foundation stone ceremonially laid in 1727. The city was designed by Vidyadhar Bhattacharya, an architect trained in ancient Sanskrit manuals on city-planning, and it officially replaced Amber as the Kachwaha capital by 1733.
Jai Singh built five Jantar Mantar observatories at Delhi, Mathura, Benares, Ujjain, and Jaipur. Each contained instruments including the Samrat Yantra (a large equinoctial sundial), the Ram Yantra (a cylindrical altitude-measuring structure), and the Jai Prakash (a concave hemisphere). The observatories at Jaipur, Varanasi, and Ujjain remain functional today.
Jai Singh persuaded Emperor Muhammad Shah to abolish the jaziya tax on Hindus in 1720 and to remove the pilgrimage tax at Gaya in 1728. He also worked to abolish Sati and to reduce excessive spending on Rajput weddings. He was the first Hindu ruler in centuries to perform the Ashvamedha sacrifice, which he conducted in 1716 and again in 1734 and 1741.
The Jaivana is a wheeled cannon created by Jai Singh before he moved his capital from Amber to Jaipur. It remains the largest wheeled cannon in the world. Jai Singh's emphasis on artillery and matchlock-armed infantry placed him ahead of his contemporaries in recognizing the shift that firearms had introduced into Indian warfare.