Short answers, pulled from the story.
The Second Anglo-Maratha War was a conflict from 1803 to 1805 between the East India Company and the Maratha Empire's confederacy of chiefs. It ended with the Company gaining direct control of territory around Delhi and in present-day Gujarat.
The war followed Peshwa Baji Rao II's Treaty of Bassein with the East India Company, signed in December 1802 after Yashwantrao Holkar defeated the combined armies of the Peshwa and Scindia at the Battle of Poona in October 1802. Other Maratha chiefs, including the Scindia of Gwalior and the Bhonsle of Nagpur, saw the treaty as a betrayal and refused to accept it.
Major General Arthur Wellesley secured the Deccan Plateau, taking Ahmednagar and winning at Assaye, while Lieutenant General Gerard Lake took the Doab and Delhi and won at Laswari. Officers named Powell, Murray, and Harcourt handled Bundelkhand, Badoch, and Bihar, with over 53,000 men available in total.
Raghoji II Bhonsale ceded the province of Cuttack under the Treaty of Deogaon on the 17th of December 1803. Daulat Scindia ceded Hisar, Panipat, Rohtak, Rewari, Gurgaon, the Ganges-Jamuna Doab, the Delhi-Agra region, parts of Bundelkhand, Broach, districts of Gujarat, and the fort of Ahmadnagar under the Treaty of Surji-Anjangaon on the 30th of December 1803. Yashwantrao Holkar later ceded Tonk, Rampura, and Bundi under the Treaty of Rajghat on the 24th of December 1805.
The war effectively ended with the Treaty of Rajghat, signed on the 24th of December 1805, when Yashwantrao Holkar came to terms with the British. Holkar had resisted since the 6th of April 1804 but lacked resources after failing to secure help from Ranjit Singh in Punjab.
Yashwantrao Holkar had already defeated the combined Peshwa and Scindia armies at the Battle of Poona in October 1802 and held a personal grievance against Baji Rao II for killing one of his relatives. When the British opened hostilities against him on the 6th of April 1804, he resisted with guerrilla warfare but did not receive the help he expected from Scindia.