Mughal Empire
The Turco-Mongol dynasty that ruled most of India from 1526 to 1857, and whose slow collapse handed the subcontinent to Britain.

Babur, a minor prince from what is now Uzbekistan, lost his ancestral city twice before he turned twenty and went east looking for a kingdom he could keep. In 1526, on the plain of Panipat north of Delhi, his field artillery and disciplined horse archers destroyed a Delhi Sultanate army several times larger. The dynasty he founded would rule most of the Indian subcontinent for two centuries, build the Taj Mahal, command perhaps a fifth of world economic output at its height, and then decay so thoroughly that a British trading company could pick up the pieces.
Akbar's bargain
Babur's grandson Akbar, who ruled from 1556 to 1605, is the reason the empire lasted. He inherited an unavoidable arithmetic problem: a Muslim dynasty of Central Asian origin governing a population that was overwhelmingly Hindu. Conquerors before him had answered by extracting from the majority and staying separate. Akbar answered by buying the majority in.
He abolished the jizya, the tax on non-Muslims, in 1564. He married Rajput princesses and made their male relatives imperial officers rather than tributaries. He built the mansabdari system, a numbered ranking of nobles that tied rank, pay, and cavalry obligations to imperial service instead of birth, and he filled it with Hindus as well as Muslims. He hosted debates between Muslim scholars, Brahmins, Jains, Zoroastrians, and visiting Jesuits, which convinced almost nobody but signaled who the empire was for.
The machine
Underneath the pageantry sat an unusually competent revenue state. Akbar's finance minister Todar Mal had land surveyed, classified by productivity, and assessed in cash at roughly a third of the average yield, with the rate fixed for years at a time so peasants could plan. Persian was the language of administration from Kabul to Bengal, which is why Persian vocabulary is fused into the languages of northern India and why Urdu exists at all.
Aurangzeb and the overreach
Aurangzeb, who took the throne in 1658 after imprisoning his father and killing his brothers, reversed the bargain. He reimposed the jizya in 1679, ordered temples destroyed in politically restive areas, executed the ninth Sikh guru, and spent the last twenty-six years of his life campaigning in the Deccan against the Marathas. The empire reached its greatest territorial extent under him and broke its own back doing it. The Deccan wars consumed the treasury, kept the emperor a thousand miles from his capital, and taught provincial governors to run their own affairs.
The long unraveling
After Aurangzeb died in 1707 the succession fights never really stopped. In 1739 the Persian ruler Nader Shah sacked Delhi, massacred its inhabitants, and carried off the Peacock Throne. By the time Robert Clive won at Plassey in 1757 and the East India Company took the right to collect Bengal's revenue in 1765, the emperor was a pensioner selling legitimacy he could no longer enforce. The last one, Bahadur Shah Zafar, was a poet in his eighties when the rebels of 1857 declared him their sovereign. The British tried him for it and exiled him to Rangoon.
Why it still matters
The Company did not conquer a vacuum. It inherited a going concern, and it kept the Mughal revenue districts, the Persian paperwork, and the fiction of Mughal sovereignty for a century because they worked. The deeper inheritance is the argument. Akbar and Aurangzeb represent two answers to the question of how a religiously plural subcontinent should be governed, and Indian politics has never stopped fighting over which one was correct.