Short answers, pulled from the story.
Mahmud II was the sultan of the Ottoman Empire from 1808 until his death on the 1st of July 1839. Born on the 20th of July 1785, he is often described as the "Peter the Great of Turkey" for his sweeping administrative, military, and fiscal reforms.
The Auspicious Incident was the forcible abolition of the Janissary Corps in June 1826. Mahmud had their barracks fired upon after the Janissaries staged a demonstration against his military reforms, and he burned Belgrad Forest outside Istanbul to eliminate survivors. The Bektashi religious order associated with the corps was also banned.
Mahmud II came to power after a rebellion deposed his half-brother Mustafa IV, who had ordered Mahmud's execution. A Georgian slave girl named Cevri saved him by throwing ashes at the assassins, allowing him to escape onto the palace roof. The rebel leader Alemdar Mustafa Pasha then proclaimed him sultan and later served as his vizier.
The Mahmudiye was a ship of the line built in 1829 at the Imperial Arsenal on the Golden Horn. Measuring 76.15 by 21.22 meters with 128 cannons on three decks and a crew of 1,280 sailors, it was for many years the largest warship in the world.
Under Mahmud II, the empire ceded the eastern half of Moldavia (renamed Bessarabia) to Russia by the Treaty of Bucharest in 1812, lost Greece through the Treaty of Constantinople in July 1832, ceded further territory to Russia after the Russo-Turkish War of 1828-1829, and saw Ottoman Algeria conquered by France beginning in 1830.
Mahmud II was succeeded by his son Abdülmecid I, born on the 25th of April 1823. Abdülmecid announced the Edict of Gülhane and continued his father's modernization program under the Tanzimat reforms.