Overall, this book is quite disappointing - much like the rest of the Colloquial language series.
Colloquial Danish starts off promising. The audio recordings are of fairly good quality, though the voice actors are unenthusiastic at best. The book progresses relatively slowly at first, giving the learner enough information to pick up the challenging nuances of the spoken language in a somewhat natural manner.
Things start to fall apart, however. If you pay attention, you'll discover that there really isn't anything even remotely resembling grammar in this book. Grammar is touched on, though only vaguely, and this book misses the grammatical exercises that one normally would expect from a beginning textbook.
The audio recordings are also very spotty. Some passages in the book have no corresponding audio text. The CDs also include extra audio not referenced in the text, most of which consists of questions and comments made in English, of all things. One wonders when the publishers of mainstream language textbooks will learn that customers would rather hear the target language more than their mother tongue.
For me, the most bothersome aspect of this book is the lack of English dialogue translations after around the halfway point. I don't understand why more difficult passages should not be accompanied by any translation at all. It's extremely perplexing, and yet is sadly a remnant of a largely broken approach to language that we have yet to move away from.
There aren't many English language Danish courses out there. This book isn't awful, though it really helps to have a background in a Germanic language - or, even better, another Scandinavian language. Perhaps one day we will have a proper introductory text for autodidactic students of Danish.