Muhammed Shah, Mughal emperor 1702-1748
December 2016 - As the Mughal Empire collapsed in the early 1700s, the Prime Minister of Britain, Robert Walpole, decided to take India over. British traders were buying and selling a lot of stuff in India, and Walpole didn't want new small countries to be at war with each other, getting in the way of British trade in cotton cloth, glass beads, and spices. Also, France was getting more and more power in southern India, and the death of Louis XIV gave Walpole an opportunity to stop that.
With Louis XV only a child, and his ministers incompetent, France soon lost southern India to the British. Then in 1757 the British army defeated a much larger north Indian army at the Battle of Plassey, showing that Indian soldiers couldn't beat the British soldiers, much better trained and with much better weapons.
After the Battle of Plassey, the British informally took over ruling the province of Bengal (today's Bangladesh and Kolkata in north-eastern India) and decided who would be the Mughal emperor. British fortune-hunters poured into India to get rich by taking bribes from local rulers and businesses. Many died of malaria and typhoid, but others got very rich. Most of that money left India and went back to England, so people in England got richer and people in India got poorer.
Officially the Mughal emperors (in the north) and Deccan kings (in the south) still ruled India. But really the British were always pushing the Indians around, making decisions and forcing them on the the local rulers, who had less and less power. Christian missionaries pressured the Hindus and Moslems in India to convert to Christianity. British governors like Lord Cornwallis pushed Indians out of power and put British men in charge of everything. In the 1800s, the British began to build railways all over India.
But the British didn't act like responsible rulers: they didn't do much to take care of the Indian people. A great cholera epidemic hit India in 1817 AD. Millions of people died. But the British government used the tax money they got in India to build clean water and sewage systems in England, not in India: they didn't care whether lots of Indian people died of cholera, typhoid, and dysentery. In 1835, the British began to tax salt, to force Indian people to buy salt from British traders instead of making it themselves.
By 1850 a lot of people in India were very upset with the British, and they fought a revolt to try to get free of British control. But the British army was still stronger, and the Great India Mutiny of 1857 only resulted in the British government taking even more power in India. In the 1860s, when the American Civil War kept the British from buying American cotton, the British began to force India to sell raw cotton instead of weaving the cotton into cloth - so again, they made less money on it and got poorer, while Britain got richer.
Learn by doing: Read Rudyard Kipling's book Kim
The British leave India - Mahatma Gandhi