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I am interested in knowing as much as possible about Eliyahu, both from oral and written tradition.
Are there any book(s) and sources that mention something that surely must have been happened but is not mentioned in the Bible?
There is a book written by Abie Rotenberg called Eliyahu Hanavi: The prophet through the prism of Tanach, Talmud and Midrash
I haven't read it, but it sounds like it would have the information you are looking for. Available from Artscroll.