British India
The first players from Europe were the Portuguese and the Dutch, however as seen in other parts of the world the French and then eventually the British controlled the seas.  The three main companies were the Dutch East India Company, British East India Company, and French India Company. Imperialism in the region had various motives.  Colonies provided markets to serve the Industrial Revolution. Motives for the countries were typically the same as in Africa, except for France.  After the loss of the Franco-Prussian War in 1871, the French were trying to regain some national pride through their colonies and imperialism
Also known as the VOC. Company granted a monopoly in 1602 for all trade between the Cape of Good Hope and Straits of Magellan. The goal and purpose was to first organize Dutch trade in the East Indies, and second to raise funds for current war against the Spanish. The VOC lasted until 1799. Its holdings were beyond India, typically found in the area of Jakarta and Java. Unlike the French and Portuguese, the Dutch were more interested in commerce than conversion to Christianity.
French felt need to push their commercial interests because of the Dutch and British. The French entered the area (1664) much later than the Dutch (1602), and British (1600). The French never really became a dominant part of the region; they eventually focused on an area which is now Vietnam, Laos, and Cambodia.
The combination of sea experience, territory, and stable government made expansion into India easy for the British. Conflict with European rivals made the decision to arm the East India Company helped the British conquer India. The weakened Mughal Emperor in 1765 made a deal with the British making them the diwan of Bengal and other territories. This deal made the British go from trading partners within the region to rulers of the region. Prior to this moment, it was the Battle of Plassey in 1757 which made it happen. Robert Clive was able to hire Indian agents to collect taxes and in turn they kept judicial authority. By 1767 this system led to greed and in 1774 the Regulation Act was passed.
The British slowly gained more and more control of India; the India Act of 1784 brought more power to the crown. The current governor of India resigned in disgust citing his loss of power from London. The next leader was Lord Cornwallis (1738-1805). Lord Cornwallis lost to George Washington in the Americas. In India Cornwallis enacted the Code of Forty-Eight Regulation in 1793. This set standards for administration, tax collection, and courts. The Cornwallis Code was the standard of rule in India until 1856. Slowly the British collected more authority in India. The British always had difficulty understanding the tribal areas and customs of the region.
The Indian Mutiny occurred in 1857-58 by Indian soldiers referred to as Sepoys who served in the Bengal army. The goal of the event was to end the British dominance over India. Many factors led to this sporadic, disorganized rebellion. Permanent Settlement Act of 1793 destroyed flourishing Indian cotton industry. India was a captive market to the British. The Act also increased the tax burden and collection techniques. All the while the British collected more land and power.
A general dissatisfaction and unease was growing within the Indian population. By 1856 the British had 43,000 troops to the Indian 223,000. Soldiers were poorly paid and little chance for promotion. The flashpoint was the 1857 Lee Enfield Rifle. Cartridges which needed to be bitten before loaded were greased from pigs and cows.  The Bengal infantry refused to use the rifle. Soldiers protested and eventually it became a full blown revolt and they marched to the key city of Delhi.  The soldiers proclaimed the Mughal ruler the new leader of India. Most of India did not know or support the rebellion. The Sepoy held onto their location as long as they could, however, British military might retook every city and punished the rebels.
The British East India Company was removed from power of India. The Doctrine of Lapse was renounced. The Bengal Army was disbanded. New relations were created with prince states. Mughal rule was eliminated. A reorganization of administration, tax collection, and education was administered.  India stayed with this system until the end of World War II.  After World War II, along with the protest movement started by Gandhi, India became a free and independent nation.