Hello guys I have a question and hopefully you can help me! I am looking for primary sources written by Europeans from the Age of Discovery up until the very end of most European colonial empires. So basically anything from the 1400's to the late 1900's. It doesn't matter which continent it's from, I'm interested in anything! Americas, Africa, Asia, Middle-East, Oceania and so on.
So far I have gathered:
For New Zealand there's an extremely good range of sources that have been digitised.
The University of Auckland hosts a very good collection of sources on the Early New Zealand Books website, covering essentially the entire 19th century.
There is another pretty good collection hosted by Victoria University (New Zealand Electronic Texts Collection) however it's less focused on primary sources, and it's harder to find books if you don't already know what you're looking for (it's a fair bit larger, and not organised by date).
Papers Past, which is pretty much all newspapers published in New Zealand is more useful for the later periods, but it goes back to 1839.
As you may have noticed, there is far more available material than you are likely to read, so it would probably help to have some goal or question to try to narrow things down. It would also be easier if you'd read a general work to help contextualise the sometimes hard to understand or actually wrong primary sources, or to at least give a basic understanding of the timeline.
Methodology aside though, as you seem to be more interested in the sources than the subjects, I'd recommend Maning's Old New Zealand, which is a pretty funny retrospective account of New Zealand in the 1830s, and is also at considerable pains to appear a less complex document than it actually is. Funny for entirely different reasons, Edward Markham's New Zealand, or Recollections of it has a very idiosyncratic style, not to mention spelling and punctuation (according to the editor, 'Few persons not actually illiterate could ever have been so poorly qualified for authorship'), and includes many sections that were once considered unprintable. He is describing a pretty similar time and place to Maning (who he describes as 'a double faced sneaking Thief' who 'would have done Honor to the back Woods in America'), and is extremely colourful. There are also a bunch of illustrations done by the author, which is always a plus. Rather a long book, but Nicholas' Narrative of a Voyage to New Zealand, is also quite good. He visited the Bay of Islands in 1814 with the first Christian mission at a time when Europeans were rather rare visitors. Rather more for if you're actually interested in the subject, but Nicholas is also a fairly interesting character (his habit of playing practical jokes on well-known cannibals is an interesting decision) and gives a lot of portraits of well-known Māori leaders as he perceives them, which is often quite different to how later history would.
Mostly based on my reading, which has been pretty slanted towards the early 19th century and the Bay of Islands. To push the time-period out a bit, I could recommend the death of Marion Du Fresne for the early explorer period, and Taranaki Punch for the Taranaki War of 1860/61. The quality of the art and humour isn't terribly high, but I think it gives as good an insight into the settler point of view, in a more entertaining way, than a lot of other sources.
If you can read Dutch the, partially, digitised collection of the Van Linschoten Vereeniging should be interesting. They publish various travelogues and ship's journals, mostly from the 17th century.
If you can't well, happily, this account of a Dutch east India Company embassy to China was translated at the time. The book also includes a general description of China, as well as accounts by various other people.
As for early colonial source in South America, the most indispensable is Guaman Poma de Alaya's Nueva Coronica y Buen Gobierno. It's almost mandatory for any book on the Andes to include an illustration from it. Poma was a Quechua noble, so not European, but it's hardly a "native" perspective. Some other important Spanish texts on the Andes are:
I can also recommend several important scientific works of Europeans documenting the physical and human geography of the Americas. The single most influential work is Alexander von Humboldt's Vues des Cordillères, et monumens des peuples indigènes de l'Amérique, which you can get a very nice scan of here, along with a searchable text only version. Nearly every other naturalist, tourist, and armchair archaeologist reference him for the next hundred years. Similarly important for Mesoamerica was John Lloyd Stephen's Incidents of Travel in Yucatan and its incredible illustrations from Frederick Catherwood. I've contextualized these and several other "academic" works in this answer, which focuses primarily on the works of the French Scientific Commission of Mexico and has a good guide to the entertaining if problematic work of a personal favorite illustrator, Jean-Frédéric Maximilien de Waldeck.
If you're interested in these kind of travelogues, I'd also recommend these. They do deal with post-colonial states, but are absolutely through the same colonial lens. You can find various versions online:
Perou et Bolivie by Charles Weiner
Travels in Peru, on the Coast, in the Sierra, across the Cordilleras and the Andes by Johann Jakob Tschudi
Perú: Incidents of Travel and Exploration in the Land of the Incas by Ephraim Squier