There are four books that J.R.R published while he was alive. Those four books are: The Hobbit and The Lord of the Rings. The Lord of the Ring was published as three separate books titled: The Fellowship of the Ring, The Two Towers, and The Return of the King. The Hobbit was the first book published in 1937, This was followed by The Fellowship of the Ring in 1954 with The Two Towers releasing a few months later in the same year. The Return of the King was then released in 1955.
There are many books that over the years have influenced the fantasy genre, but in my opinion, The Hobbit and The Lord of the Rings is the biggest influencer of the fantasy genre.