I'm working on my research paper. My subject is quite original and I even had difficulties to find a supervisor. In short, I found a fairly recent book on the Internet (2017), which is exactly what I am looking for, but it is not available in the libraries of my country. Could I ask the author to send it to me by email or even to send me some chapters?
Certainly you can ask. There is nothing wrong with that. If you explain a bit about your use and the restrictions you face it might make it more likely that the author might try to help you.
But the author might not be able to comply with your request due to contractual arrangements with the publisher (if any). So, you might get a reply that starts out "Sorry, but..."
On the other hand, I'm surprised that libraries don't have access. I would guess that if you take your request to the librarian him/herself, you might learn that copies of nearly everything can be borrowed. Librarians have a vast, legal, network of sources for academic/scientific works. Even my town library, which has no formal relationships, can find just about anything I need, though the sources are usually all in this country.
But there are no ethical issues about asking. Etiquette only requires politeness and being honest about your needs.
I recommend, as others have, starting with a librarian. I'd follow up with looking for papers by the same author. Sometimes, the reference list of books is available, and you can pore through that getting works that are seminal.
I'm not sure where I am with respect to asking. I lean toward not doing it. "You can always ask" is certainly true, but sometimes, merely asking is rude. I don't know where I draw the line. I just asked an artist for permission to use a particularly apt cartoon, with attribution, in a course lecture. The artist was absolutely thrilled that I asked for permission, and sent me a higher-res copy! That said, here's an artist, who makes a substantial part of his living doing this sort of stuff, and I asked him for a free use. The way I justify this in my head was "I don't really need this, and it's not something I'd pay more than a few dollars for, and if he says no I just won't use it (and I wouldn't!)" Perhaps the better way to have done this was to contact him with the question "Is there a reasonable way I can license this for this low-volume use?"
Working for a university library purchasing resources, I am asked this question by students and academic staff fairly regularly.
As others have implied, one of your options in getting access to the ebook is to contact the library with which you are affiliated, whether this is via an InterLibrary Loan request, an email to its resources department (which exists in all libraries in some form or another) or a question at the front desk. From my experience, these requests eventually get funnelled to a librarian, who is usually tasked with asking a book supplier to make the ebook available for purchase online, or directly asking the academic whether a copy could be made available to the library.
Importantly, the library will have the money to make a purchase for you, if necessary. However, whether it will pay for you may depend on its purchase and lending policies. Moreover, if copyright issues arise or the library decides that they'd like the book to form part of their collection (and therefore available for others to use), then they'll be in a better position to negotiate these processes on your behalf.
Of course, there's no harm in contacting the academic yourself... In similar situations in the past I've contacted academics expecting a hefty fee only to find they're all too happy to provide their materials for free!
Someone asked me once if I could send them a free digital copy of a book I had published recently and I was happy to send it to them for a few reasons:
A.) I'm happy that someone actually wants to read it as I put a lot of time and effort into writing it.
B.) If the person likes it, they might tell other people and so get good publicity for it.
c.) It's only one book. The amount of money you would get for selling one copy of a book is negligible, so you are not really losing anything by giving them a free copy, especially if the person seems genuinely really interested and respectful.
So I would definitely just ask, they might even be pleased to send you a free copy.