There are numerous books on trout fishing. Here is a personal recommendation for the beginner (in italics are my reason for recommending):
John Goddard and Brian Clarke: The Trout and the Fly
(understanding trout)John Goddard: The Waterside Guide
(fly fishing entomology)Martin Cairncross, John Dawson and Chris Ogborne: Success with Trout
(fly fishing on stillwaters)Charles Jardine: Sotherby's Guide to Fly Fishing
(fly patterns)Peter Mackenzie-Philps: Fly Casting Handbook
(fly casting)Mel Krieger: The Essence of Flycasting
(fly casting)Steve Parton: Boat Fishing for Trout
(lure fishing from boats - very interesting read)
Anything and everything you can lay your hands on.