If you are serioius about fly fishing literature, you should read some or all of the books by these authors (in no particular order of importance):
1. Ernest Schwiebert
2. Thomas McGuane
3. Nick Lyons
4. John Gierach
5. Robert Traver, aka Paul Voelker
5. James Babb
6. Harry Middleton
7. Christopher Camuto
8. Paul Schullery
9. Charlie Fox
10. Roderick Haig-Brown (possibly the greatest fly fishing writer of the 20th century.
This is not meant to be all inclusive. There are some really good writers out there today, including a lot of how-to books by Caucci, Borger, Wulff, LaFontaine to name a few.