Where did the Dutch claim or colonize territory?

Answer 1

The Dutch in the form of the Netherlands or earlier the United Provinces had a substantial colonial empire.

The Dutch East India Company (VOC) and later the Dutch State controlled what is now Indonesia (Dutch East Indies) and the island chain it is part of in south east Asia. This was the most important holding and they only gave it up after the World War Two. They also, oddly, had control of what is now Taiwan for a period.

They also colonised bits of what is now the north east US, New York was New Amsterdam before being captured by James Duke of York and most of Dutch North America was absorbed into the new British colonies.

They also had holdings in the Caribbean (and still have a couple of islands) and the north east coast of South America.

The Dutch also set up Cape Colony - which was taken from them by the British (twice) and became the modern State of South Africa eventually - and a couple of other colonies in Africa.

It should be noted that since Holland/Dutch Republic/Netherlands/United Provinces went through a lot of changes of control and territory itself (arguably taking over Britain at one point and was nearly absorbed into France at another.) their colonial empire waxed and waned with the fortunes of the mother country and they didn't hold all of the above at the same time.

Answer 2

south Africa