Ernest Hemingway writes a lot about fishing. My favourite is a short story called Big Two Hearted River. Brilliant story about a young man finding healing in the details of a fishing trip after a war in which he suffered and lost friends. Well worth tracking down and savouring.
Very enjoyable was Fishermans Winter, yes it was descriptive in it's writing but not over flowery. I've got the reprinted 2014 edition with the forward by Nicky Lyons. Considering it was first published in 1954 it did not seem that dated. Nice to read about a part of the world I know very little about, I'll order the other three in the series shortly. Thanks to JayP for the prompt.
I'm surprised nobody has mentioned 'Fly Fishing by J R Hartley' yet. Anyone of a certain age will have had that book and/or the name of the author quoted at them (ad nauseum) at the very mention of having fly fishing as their hobby!