Here we go:
For flies: "Fishing Atlantic Salmon; the Flies and the Patterns" by Joseph D. Bates and Pamela Bates Richards published by Stackpole
"Modern Atlantic Salmon Flies" by Paul Marriner published by Frank Amato. I think there's a new edition.
"Salmon Fishing - a Practical Guide" by Hugh Falkus. Like Ard, I've heard the Topher Browne's book is good. Dunno, haven't seen it.
For stories and reminescences:
"Six Salmon Rivers and Another" and "The song of the reel" by George Frederick Clarke
Lots of others. Personally, in the case of the "how-to" books, I find there is not much new under the sun, and that the older books are more interesting and even entertaining. I always like Lefty Kreh's observation that "an expert is anyone with his own slide projector more than 50 miles from home." Lots of wisdom in that one.
Have fun reading! Oh, and I'm sure there are beaucoup DVD's out there, too. But atlantic salmon fishing is really quite simple. Cover the water.
There are plenty of books out there on the topic of fishing for atlantic salmon!