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Portugal establishes first colony in Africa. They then established a large number of cities along the coast of Africa. These colonies were small cities that the Portuguese would use to trade from. They did not try to conquer the country.
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Columbus reaches the Bahamas from Spain. This is the first time Europeans have reached the Americas.
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First Spanish colony is established in South America. They soon spread to conquer from Mexico to Chile.
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Brazil colonised by the Portuguese. This is the only Portuguese colony that was eventually turned into a country.
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Portuguese establish a colony in Goa, India. They soon spread their trade through to India.
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Spanish conquest of the Philippines.
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British land in North America and start building colonies.
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Dutch conquer Java (Indonesia). They burn down the capital and build a new one. They soon become the only people trading in spices, which come from Indonesia.
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French colonise Canada. Move south through USA to Caribbean. In the process, they conquer a huge amount of what is now the USA.
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British colonise the Caribbean.
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Dutch buy Manhattan Island and call it New Amsterdam. At this point, they have small trading towns all over the coast of North America (much like the Portuguese in Asia and Africa)
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British enter India. Over the next 250 years, they take over all the way from Pakistan to Myanmar.
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British begin to colonise Africa. They get most of the middle of the continent.
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Brazil becomes independent. By this time, most of South America is independent.
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The French colonise Indochina (Cambodia, Vietnam, Laos)
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Germany and Italy begin looking for colonies in Africa, but most are already taken.