Q: What books have been written without specific letters, vowels, etc.?
Such a book is called a lipogram.
A novel-length example in English (omitting e) exists, titled Gadsby. (E. V. Wright, 1939)
Georges Perec wrote a French novel titled La Disparition which does not contain the letter 'e', except in a few bits of text that the publisher had to include in or on the book somewhere -- such as the author's name :-). But these were all printed in red, making them somehow ``not count''.
Perec also wrote another novel in which `e' was the only vowel.
In La Disparition, unlike Gadsby, the lipogrammatic technique is reflected in the story. Objects disappear or become invisible. We know, however, more or less why the characters can't find things like eggs or even remember their names -- because the words for them can't be used.
Amazingly, it's been ``translated'' into English (by Harry Mathews, I think).
Another work which manages to [almost? adhere to restrictive alphabetic rules while also remaining readable as well as providing amusement and literary satisfaction (though you have to like disjointed fiction) is Alphabetical Africa by Walter Abish. The rules (which of course he doesn't explain, you can't help noticing most of them) have to do with initial letters of words. There are 52 chapters. In the first, all words begin with `a'; in the second, all words begin with either `a' or `b'; etc, until all words are allowed in chapter 26. Then in the second half, the letters are taken away one by one. It's remarkable when, for instance, you finally get `the' and realize how much or little you missed it; earlier, when `I' comes in, you feel something like the difference between third- and first-person narration. As one of the blurbs more or less says (I don't have it here to quote), reading this is like slowly taking a deep breath and letting it out again.