1498 - Portuguese under Vasco da Gamma arrive at Kappad (near Calicut (Kozhikode), Kerala) in the kingdom of Saamoothiri (I'm unsure if this is the name of the kingdom, but it is at least the name of the ruler, the kingdom centered on Calicut and ruled over the surrounding areas of Kerala). Establishing the trade route between Portugal and India via the Horn of Africa (there are some sources which suggest that Greeks knew of this route before hand, but none of the sources are very strong).
1510 - Portuguese under Afonso de Albuquerque capture Goa and establish a Portuguese colony in the city of Goa and its surrounding area.
1600 - British East India Company founded as a joint-stock company with a 15-year monopoly over British trade in the East Indies (India and SE Asia) in its founding charter, granted by Queen Elizabeth.
1602 - Dutch East India Company founded (VOC based on its Dutch initials) as a joint-stock company with a 21-year monopoly over Dutch trade in the East Indies in its founding charter, granted by the Dutch States-General.
1605 - Mughal Emperor Jahangir begins reign.
1605-1627 - Reign of Mughal Emperor Jahangir
1619 - Mughal Emperor Jahangir grants the British East India Company permission to trade in his territories at Surat (in Gujarat).
1627 - Death of Mughal Emperor Jahangir
1627 - Mughal Emperor Shah Jahan begins reign
1627-1658 - Reign of Shah Jahan
1639 - First British factory in India established at Madras, then called Fort St. George. It was a factory in the sense of the word meaning warehouse.
1658 - Mughal Emperor Shah Jahan overthrown by his son, Aurangzeb. Beginning of the reign of Mughal Emperor Aurangzeb.
1658-1707 - Reign of Mughal Emperor Aurangzeb
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