I remain a fan of
Elementary Harmony by Robert W. Ottman. It does help to be able to read notation at an elementary level to use the book; but, for those who don't, the book covers basic notation in the first chapter. For players who don't read music notation and want to learn theory, plan on learning some basic notation if you are going to use a book. I believe Ottman will still be valuable to you, but you will spend more time--though you will learn a lot--in the first chapter.
Like most long-standing books on music theory,
Elementary Harmony is geared toward classical music; but it's done using the simplest possible examples, so the elements are understandable even if you don't plan to analyze many Bach chorales.
The real strength of this book, IMO, is it's completeness. It was a music theory textbook for me in both high school and college and now, decades later, it is my go-to reference work on music theory when I have a new question (heaven knows I've never forgotten anything over the years

).
I haven't used the newer editions which have accompanying workbooks and CDs available; but both those items should make the text significantly more accessible by itself (i.e., outside the classroom). New copies can be expensive, but if you search the 'net, there are discount outlets and high-quality used copies available at significant savings.
Bluesy Soul
