"One Hundred Fifty Songs With Just Three Chords," Ekay Music, Inc., 223 Katonah Avenue, Katonah, NY 10536, 1990, ISBN 0-943748-47-X, $16.95 (in 1995)
But as several people have pointed out - why bother. Borrow a copy of "The Ultimate Country Fakebook" from Mel Bay - any of the last 4 editions - and you get 700 songs you can play with just three chords.
Talk about a rip-off.

This has been a good thread, although I think WyoWoman asked for a sip, and several of us have aimed a firehose at her. I'm sure she has the good sense to duck, when necessary, and won't begrudge the rest of us some fun.
Since I'm not too much into heavy musical theory, I won't comment on most of the hard-core lessons there, but some might be interested in some side notes.
Several people have alluded to the "do-re-me" note names. Traditional lore is that back in the olden times when only the monks s(w)ung, and everything was in Latin, a common liturgical "song" had the notes of the major scale in ascending order. The first syllable of each of the words sung to this liturgy came into use as names of the notes. "DOminus REmulus MIxedicus FAcetius, etc." Obviously I don't remember the Latin, but you get the point. Since everyone knew the song, it made it easier to remember the pitches. It's a little like "Joy to the World" where the same scale is all in perfect DESCENDING order.
I've noted some discussion also of why some intervals sound "good" and some sound "terrible." Most of this discussion has been close to the point, but has sort of floundered around it. Some of us might be better off to recall the mountain dulcimists' mantra, "Find a Pleasant Tone," and leave it at that. My SO has been working on that for quite a while now, and may be ready for the next step ("find the same pleasant tone everyone else is playing"). For the very few of us who might benefit, I would suggest "Fundamentals of Musical Acoustics," Arthur H. Benade. Reprint of the 1976 2d edition by Dover Books is about $16. Another suggestion would be "On the Sensations of Tone" by Hermann Helmholtz. The original dates back to the 1870s, and poor Hermie made a few minor mistakes because his equipment was not quite up to modern standards; but for the most part his presentation is clear. The current Dover edition, probably about $15 or $18 now, is a reprint of the 2d English translation, which was made from the 3d German edition. It has stood up well. These books are suggested only for those who want the satsifaction of understanding "why" the world works like it does, so I don't suggest that anyone leap into them with the expectation that it will improve their playing. Some parts of them can be pretty heavy going, although neither book is "mathematical." And you only need to look at what is helpful to you. Most of us would really rather go practice a bit more - and that's good for the soul too.

John