So many good suggestions and some of my favorites have already been mentioned. One of the things to consider is "modern" or "traditional". A lot of folks divide fly fishing into "pre-movie and post-movie" (A river runs through it) and often in the post-movie crowd you find people that take themselves way too seriously and believe "real" flyfishing is XYZ.
The same can be said about books about flyfishing. Some writers simply make more of it than it is and some can get a bit preachy towards certain techniques. I tend towards older writing when fishing was largely a choice of bait casting or fly fishing. I've also been at it long enough (40+ years) that I tend to enjoy the stories more than the how-to books.
Look up books by Roderick Haig-Brown - my time in the PacNW really made me like him
Robert Traver, as mentioned before, is truly a favorite in the UP of MI.
John Gierach can be very good but can tend towards that preachy "dry fly and bamboo only" writing. I actually find his stuff after he quit drinking to be more that way but I do enjoy it and tend to buy all his stuff. It made time at sea pass well.
I will also put out anything by Scott Waldie (RIP) that is less about flyfishing directly but more about life in small town MT where people also fly fish. - I often reach to read a story or too as I reflect up on my life here where I make money but live less than I want to.
https://www.amazon.com/Scott-Waldie/e/B001K8EU8Y/ref=dp_byline_cont_ebooks_1 
