The authors have taken a textbook-like approach to language instruction. The material is neatly divvied up into (presumably weekly) lessons, each with a grammar topic, vocabulary list, and translation exercise. I have learned a language this way before, a dead language. While the skills I learned then permit me to pedantically plod my way through Ceasar, Cicero on a good day, or Vergil if I am lucky, I don't think I would make much headway if I fell through a time warp and had to find my way to the Forum. If, however, you intend to communicate with Russians living in the same century as yourself, there are better ways.
In fairness, the audio cassettes are helpful, and the systematic approach builds basic skills very well while avoiding pitfalls. My pronunciation was, according to a Russian-speaking co-worker, nearly free of any accent after only a few chapters. That was mixed blessing though, as Russians (in Russia, that is) routinely overestimated my skill in the language. Grammar is covered rather well, though Kemple's Russian grammatica is much better.
Drill materials are sorely lacking. You get Russian conversation (albeit contrived to fit in the given vocabulary) pretty much dropped on you as whole language. None of the pedagogical decompositions "This is a book...this is a blue book...here is a book...here is a pencil..." that mirror the way we learn language naturally (or for that matter, the way we learn karate, or baseball, or any other working skill).
The authors don't seem to have put much thought into prioritizing vocabulary. You can master all 20 chapters and still not know how to say "be careful", or "stop kicking me". Tellingly, one of the chapters is dedicated to women's issues in Russia (in case that comes up while talking to the cabby) but nothing on automobiles, bicycles, carpentry, plumbing, or electronics, tellingly betraying an academic point of view whose bias pervades the whole course. I found myself, in utter desperation, abandoning the course about halfway through and building my own study materials: flash cards, vocabulary lists, speaking exercises, and audio tapes dictated by myself.
In short, I found the earlier parts of the book useful in building basic skills. If you have other aids (or a human instructor) to help with practice drills, this course may still be useful. If you are an instructor, its weekly-lesson format may be worth considering as the core of a language course, but you are being cruel to your students if this is the only book you use. As a self-study course however, I have to say that newer products have come along that do the job better.