Here's a long answer for your question.
Basically, in 1947, as the British Empire left India, the British government partitioned India after a decade of protests and political maneuvering by the main Muslim political party of India, the Muslim League to create a separate state for the Muslims of India. Pakistan, the new state was formed out of the provinces of Baluchistan, Sindh, the Northwest Frontier Province, and out of the Muslim majority regions of the provinces of Bengal and Punjab. However, large parts of India, the Indian princely states, were only indirectly controlled by British, and had the right to choose which nation they wanted to join, based on the beliefs of their people. Maharaja Hari Singh, the Hindu ruler of mostly Muslim Kashmir wanted to remain independent, as he was being courted by the rulers of both India and Pakistan. However, the people of Kashmir led by Sheikh Abdullah, leader of the National Conference wanted to join India. The Pakistani military decided to settle this through force and sent Afghani irregular troops in to Kashmir in 1948. Upon hearing this, he appealed for Indian protection, and acceded to India's rule. India did this, sent military forces into the region, and prevented all of Jammu and Kashmir from going into Pakistani hands, though about 1/3 has been occupied by Pakistan ever since. In fair elections, Sheikh Abdullah became the leader of Jammu and Kashmir (or at least that part not occupied by Pakistani forces), and in 1959 the popularly elected Jammu and Kashmir state assembly agreed to accept the jurisdiction of the Supreme Court of India over their internal affairs, completing the process of joining India. Meanwhile, it had become an article of faith in Pakistan that all of Kashmir wanted to join Pakistan, and in the meanwhile India (rightfully as per the Jammu and Kashmir Instrument of Accession, and India Independence Act claimed all of Jammu and Kashmir. In 1962, China invaded India and took over 38,000 sq km of Kashmir, and in 1963, Pakistan gave 2,000 sq km of Kashmir to China. Here's an Indian source referring to both of the above.
In 1965, a war between Pakistan an India an inconclusive war was fought over the status of Kashmir, and also a border dispute along the southern edge of the border.
Meanwhile, Pakistan's internal affairs were causing more problems. From the beginning, they declared themselves as a Muslim state, with Islam as the state supported religion, and made Urdu, a minority language spoken by about 8% of the West Pakistani population the national language. Both of these actions caused alienation amongst the East Pakistani population, almost entirely Bengali speakers, and about 25% Hindu. The military rule that Pakistan fell into consisted of rulers from the West Pakistani province of Punjab, and their actions were seen as favoring their home province and West Pakistan to the detriment of East Pakistan. In 1970, Pakistan held its first elections with universal suffrage, and Sheikh Mujib ur-Rahman, of the Bengali Awami League won almost all the seats from East Pakistan and in doing so one a majority of seats in Parliament. He campaigned under a slogan of regional autonomy for the provinces of Pakistan. The military was threatened by this arrested him, and installed the leader of the largest West Pakistani political power in charge. They then started widescale oppresion of the Bengali people, drove 10 million of them, mostly Hindus into exile in India, and killed 2 million Bengalis. The Indian economy was strained to the limits by the massive refugee influx, and started supporting Bengali freedom fighters fighting for the freedom of Bangla Desh (Bengali Nation). Finally, on December 3, 1971, Pakistan launched a preemptive attack on India to get them to stop supporting the Bengali rebels. India fought back and on December 16 (less than two weeks later), the Pakistani army leader surrendered to Indian forces which occupied all of East Pakistan, and the nation of Bangladesh formally came into existence. More information on the events that led to the independence of Bangladesh.
There was also some fighting along India and Pakistan's western border. A year later, Prime Minister Indira Gandhi of India and President Zulfiqar Ali Bhutto of Pakistan met at Shimla in India and agreed that all disputes between them would be settled bilaterally.
A few years later Zulfiqar Ali Bhutto was over thrown by General Zia ul-Haq, and later executed. Zia ul-Haq's regime was noteworthy for the Islamization of Pakistan, and support for the Afghan resistence. In 1988, the Soviet Union left Afghanistan. One year later, some Kashmiri leaders, disatisfied by Indian rule started an armed rebellion against Indian rule. Pakistan always claimed that it only supported them morally, but realistically, it was physically impossible for them to have gotten support from anywhere else. Many of these leaders wanted either an independent state, or union with Pakistan. These Pakistani supported terrorists like their army brethren in what is now Bangladesh, targetted the Hindu and Sikh minorities especially, and drove 95% of them from the Kashmir valley, into refugee camps in the Hindu majority Jammu region of Kashmir. Since then, 70,000 people have died in the violence, most of them innocent civilians massacred by the terrorists. The "militancy", to use an Indian English term, wrecked the economy of the state, despite an influx of government support. Increasingly, the terrorist campaign has had an increasing Islamic focus, targetting both the Hindu and Sikh minorities, and also the more relaxed sect of Islam followed by most Kashmiri Muslims, Sufiism. In 1999, Pakistan sent troops across the Line Of Control, that forms the defacto boundary between India and Pakistan, in Kashmir, to capture mountains overlooking a major road. After about 2000 dead (on both sides), and American pressure, Pakistan was forced to reign in troops (who it claimed were indigenous Kashmiri freedom fighters). A few months later, the brainchild behind this operation, General Pervez Musharraf, staged a successful coup, and became Pakistan's leader. Despite attempts at diplomacy, the situation in Kashmir didn't get better, and after terrorist attacks on the Kashmir assembly and Indian Parliament, staged by Pakistani nationals, possibly with the support of their government, the current military build up started. A few months ago, Jammu and Kashmir, in their most recent elections
threw out the National Conference which had ruled them for so long. The future is left to be seen.
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