Short answers, pulled from the story.
Shivaji, a Maratha aristocrat of the Bhonsle clan born in 1630, founded the Maratha state. He was crowned Chhatrapati (sovereign) of the Maratha Kingdom in 1674 after establishing control over many forts in the western Deccan and successfully resisting Mughal expansion.
At its zenith in 1760, Maratha territory covered over 2,500,000 square kilometers, roughly a third of the Indian subcontinent. The confederacy extended from Punjab in the north to Hyderabad in the south, and from Kutch in the west to Oudh in the east.
The Peshwa was the Prime Minister of the Maratha Empire, a position originally created by Shivaji to delegate administrative duties. Prior to 1749 they served terms of 8-9 years; afterward, the Bhat family became hereditary Peshwas and the de facto rulers until the empire ended in 1818.
The Marathas were defeated by Ahmad Shah Durrani's forces on the 14th of January 1761, after the Jats and Rajputs refused to support them. The Marathas had alienated these groups through heavy taxation and interference in their affairs, and Raja Suraj Mal withdrew before battle, cutting off Maratha supply chains.
The British destroyed the confederacy through the Second Anglo-Maratha War (1803-1805) and the Third Anglo-Maratha War (1817-1818). After Peshwa Baji Rao II signed the Treaty of Bassein in 1802 accepting British protection, war became unavoidable. By 1818, the Peshwa was exiled to Bithoor near Kanpur and the British controlled most of the Indian subcontinent south of the Sutlej River.
Wellesley, after defeating the Marathas, warned British officers never to let Maratha infantry attack head-on in close combat, saying any army that did would cover itself in utter disgrace. He described their artillery as so powerful it would be impossible to maintain a camp against it, and he held their infantry in utmost respect even after becoming Prime Minister of Britain.