Overall, I consider this book to be a good starter to lead you on to mastering the Greek language, and would work well alongside a comprehensive grammar book, a vocabulary book and some other listening exercises/material (and of course a taught course with a native speaker).
The sequence that the materials is presented in is logical for someone who is trying to master Greek, taking you through basic introductions and greetings to more complex interactions. Unlike other reviewers, I do not consider the dialogues given to be irrelevant. Quite the opposite in fact. But this must be considered in the context in which the book is written - for those who want to learn Greek properly, and not for those who want a few phrases for going on holiday. For this a language-learning book is inappropriate, and a phrasebook is much better - the Lonely Planet phrasebooks are excellent for this purpose.
It is often difficult to make dialogues in language-learning books not appear forced, because the language used will always seem simple compared to the language you would use in a normal conversation. However for someone who is used to learning a lot of languages, the order that you are taken through seems logical - and accords to the European Parliament's recommendations on language learning.
To comment on another reviewer's comment about learning the Greek script, most of the first 9 chapters have spellings both using the Greek aphabet, and using the transliterated versions - including all the dialogues. If you are wanting to seriously learn Greek, then you need to master the alphabet as quickly as possible, but you are not thrown in head-first as the previous reviewer would suggest. If you don't want to, and just want some basic understanding, then the Teach Yourself Beginner's Greek might be a better option.
The main problem I have with this book, and the reason why I don't give it 5 stars is the number of errors in it, and the fact that you are sometimes asked to 'practice' things that you haven't learnt yet. The errors are especially significant in the answers to practice materials, and there are quite a lot of them. Also, even in the first chapter, you are asked to 'practice' things that aren't taught until chapter 2. To be honest, this is rather poor, and it mars an otherwise good book.
If you're looking to master Greek, this is a good place to start, if you're looking for a few phrases before a trip to Greece, then look elsewhere.