While I'm not technically finished with the book, I felt ready for a review to get this off of my currently reading shelf. The nice thing is this book doesn't assume any understanding of music theory and so goes into the basics. Then it describes the notes and positioning on the Mandolin. However, it doesn't go into a lot of detail on how to play correctly.
The best thing this book does is give you a series of progressively more difficult pieces to play through. I'm taking it slowly as I'm teaching myself. I think it will take me a while to reach the end of the book, but I'd like to think that by the time I reach the end (in a year or two) I might be fairly proficient.
Supplement this book with YouTube technique videos or other books and you might be in a good position to learn the instrument.