Before I bought this book I looked at several other introductory books on Russian. I chose this one because it is clear and concise, and packs a great deal of learning into each chapter. If you are sufficiently determined, in an astonishingly short time you should have a grounding in grammar and a vocabulary of about 1500 of the most commonly used words, and be able to read and write confidently in Russian about everyday subjects. It takes you up to intermediate level, which I think means to about GCSE level. The last few topics introduce current affairs vocabulary, and have an A-level feel to them.
I understand this is the book that Cambridge University recommend to complete beginners in Russian studies. Be warned then: you will need either a Russian tutor or the kind of motivation and self-discipline that you would expect from a Cambridge student. There is little space devoted to teaching you either pronunciation or Cyrillic writing. It is simply assumed that you have other ways to learn these (e.g. the optional extra CDs or cassettes). There are few opportunities to consolidate your understanding (e.g. revision exercises): you are expected to grasp every grammar point and learn every word the first time you encounter it. There is a good English-Russian, Russian-English vocabulary section at the back, but the grammar topics are poorly indexed. Expect this book to become dog-eared as you thumb through it searching for the page where the grammar point that you need but can't quite remember is explained.
If you want to learn simply a little conversational or tourist Russian then this book is not for you. Buy this book if you want to learn written Russian to intermediate level, and have access to a tutor or previous experience of learning a language on your own. Buy the accompanying CDs or cassettes if you feel rich, otherwise look for other sources of spoken Russian to help you learn pronunciation. You will probably need to buy a grammar reference book later in your studies which covers this material.