Sorry for the delay in posting in these - I hope nobody minds if I write some of these Indian topics. I am fairly interested in Indian numismatics. My hope is that, within my lifetime, India will become a wealthy nation, and Indian coins and banknotes will explode in value. Until then, I am slowly accumulating...
The topic here is Numista's various listings for India under European influence. India is a large place, so many European powers laid claim to parts of the country during the colonial era - some were more successful than others.
First, Europeans established coastal forts and trading posts - it was only in the 1800s that the great empires began drawing borders and annexing what lay further inland. Most of the wannabe powers in India never made it to that second stage, so their holdings in India only ever amounted to a few seaside forts, and coinage from those territories is thus quite rare.
Danish India
What a cozy empire!
Believe it or not, Denmark was once a serious power - that's how it managed to grab Greenland and the Faroe Islands. The Danish Empire was never particularly vast, but it did maintain a few small colonies in improbable locations. One of these locations was India. The Danish flag (the world's oldest) once flew over Serampore (today part of West Bengal, population 797,955), Tranquebar (today Tharangambadi, part of Tamil Nadu, population 23,191), and the isolated Nicobar Islands (population 36,842). Denmark was allowed to keep its little outposts as long as it didn't cause any trouble, but unfortunately all of Europe devolved into trouble during the Napoleonic Wars. Tranquebar was finally bought out by Britain in 1845. Because of Tranquebar's small size even today, coins issued for the colony there are highly uncommon. (Serampore may be large today, but under Danish rule it was just another fort.)
Dutch India
The Dutch East India Company is best known for its presence in Indonesia, but was also active in India
The Netherlands were well-known for their domination of maritime trade in the early modern period, and the Dutch colonies in India were of some importance. The Dutch took away Portugal's old colonies in India (including Sri Lanka) and started doing what they did best - making lots and lots of money. However, the economically-minded Dutch were unable to dominate their Indian neighbours militarily, just as the newly ascendant British began to expand their empire. Caught between native armies and the British navies, the Dutch were totally uprooted by 1825 - luckily for them, they still owned the Dutch East Indies, now Indonesia.
French India
Wikipedia illustrates these colonies with a postcard
The French also established some minor holdings in India. Because France had a robust presence in Europe and frequently fought the British to a draw, it was spared much of the humiliation faced by smaller colonial powers, and kept a toehold in India until 1954 - but these colonies, once again, consisted mainly of smaller cities on the coast. The largest of these cities was Pondichery, now Puducherry, population 654,392. Because Pondichery was acquired by India after that nation gained independence, it is a "Union Territory", ruled directly by the Indian federal government.
Although French India lasted until 1954, the colony did not have any distinct coins issued for it after 1837.
Portuguese India
Shield of Portuguese India
The Portuguese were the first European power to lay claim to parts of India, first arriving in 1505. Unfortunately, Portugal peaked too early. The port of Goa, once an important administrative center, gradually declined in importance, and most of Portugal's holdings were lost to the British and Dutch - except Goa (and a couple other very minor exclaves). In 1947, when India gained independence, the Portuguese refused to relinquish the Indian portion of their rapidly diminishing Imperio. Peaceful protests and various international pressure tactics achieved nothing - the only way to take Goa would be from Portugal's cold, dead hands.
A quarter tanga from 1881
The last vestiges of Portuguese authority in India
Portugal, with its small population, could not stand up to India for long. In 1961, the Indian army unexpectedly arrived in Portuguese India. Back in Lisbon, Salazar, the leader of Western Europe's longest-lasting dictatorship, sent orders to the small Portuguese garrison to honourably fight to the death. The Portuguese, numbering only 3,300 against an Indian force of 30,000, wisely ignored those orders and quickly surrendered.
This is the story of the smaller powers in India - in the interests of brevity, the all-important British presence and the state of today's Indian Republic will be left for later. As for the Mughal Empire, the Princely States, and the countless ancient kingdoms... I don't even know where to start, and invite all of the people who keep posting stunning coins from these places to contribute to future threads!