I'm an absolute beginner, pretty much, particularly with the Russian language. And after reading the first 3 chapters (yes, I didn't get far) I still had enough to introduce myself and impress the people I was visiting in country Russia. (Though I'm still a long way from actually conducting a conversation or asking anything really useful).
The CDs are a necessity with this book as the dialogues are written entirely in Russian script. Whilst one can supposedly infer the pronunciation of Russian from the script I would say that Russian is not too dissimilar from English in that some words are pronounced a little differently from how it is strictly written.. (it's hard to guess which syllables are almost skipped over completely, and which are vital). So CDs help with reading the Russian script to understand how it should sound.
It did help that I bought the associated Russian Script book in the Teach Yourself series. If anything I was able to easily identify post offices once I got to Russia!!
The CDs have an American sounding introduction, but the exercises themselves sound like a well-versed English woman is making the explanations.