Portuguese: Vasco da Gama reached Calicut in 1498, opening the direct sea route to India. Francisco de Almeida and later Afonso de Albuquerque (who captured Goa in 1510, making it the capital of Portuguese possessions in Asia) established Portuguese dominance in Indian Ocean trade for much of the 16th century. Portuguese power declined from the 17th century, though Goa, Daman, and Diu remained under Portuguese control until 1961.
Dutch: The Dutch East India Company (VOC), founded 1602, established trading posts at Surat, Masulipatnam, Pulicat, Chinsura, and elsewhere; they were eventually more focused on the Indonesian spice trade and gradually lost ground to the English in India, ceding their last Indian possessions after the 1795 Treaty and further losses following the Napoleonic Wars period (Anglo-Dutch Treaty of 1824).
English East India Company (EIC): Chartered by Queen Elizabeth I on 31 December 1600. Captain William Hawkins visited the Mughal court under Jahangir (1608–1611); Sir Thomas Roe secured a farman (royal decree) granting trading rights (1615–1619). The English established factories at Surat (1613, first English factory), Madras/Fort St. George (1639), Bombay (received from the Portuguese in 1661 as part of Catherine of Braganza's dowry when she married Charles II, transferred to the Company in 1668), and Calcutta/Fort William (founded by Job Charnock, 1690).
French: The French East India Company was founded in 1664 under Colbert's initiative; established Pondicherry (1673, founded by François Martin) and Chandernagore. French ambitions in India, especially under Governor Joseph François Dupleix, clashed directly with the English in the Carnatic Wars (three wars, 1746–1763) fought largely as a proxy for the wider Anglo-French rivalry in Europe.
Danish: Established minor settlements at Tranquebar and Serampore, later sold to the British in the 19th century.