Will any ebook work on a Kindle?

Hello, I have recently been using my mother's old kindle. I was using it to read a couple of books from a site, but now I want to read a specific book that no site has.
Now, here is the problem, I don't know much, to basically anything, about how the kindle and I really want to know if any ebook will work on a kindle. I found a place to download the book I want, but I can't figure out if once I download it to my computer, if it will be transferable and readable on the Kindle.
Can someone out there please help me and tell me if any ebook will work on a Kindle? If not, then how do you tell?
Thank you for your help:D

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