I think we can learn
about Tolkien's Elvish languages. You can learn about them, and you can learn about how, over the many years, Tolkien changed his mind concerning them [even altering already published details here and there], but you can't learn to speak them like other Primary World languages, even a language like Latin.
What you see in the films and often enough on the net is a simplified 'patchwork' version of Sindarin or Quenya, called Neo-elvish, and it might be giving the false illusion that one can learn Quenya or Sindarin, as in learn to speak these tongues. I recommend reading...
http://www.elvish.org/FAQ.html... and especially
Elvish as She Is Spoke linked from this FAQ.
I have found it rewarding to learn some things about Tolkien's languages [I am no trained linguist or expert], and you can learn something about them by looking at certain Neo-elvish courses; but I would also recommend keeping in mind the nature of these courses and the overarching caution presented in the above FAQ and essay.
And if one disagrees with the characterizations in the FAQ and linked essay, fine of course.
But I agree with them. Well, obviously