To complement the other review, *Wilding* and *Abbott and Mansfield* are the two books I began Greek with in 1998. I liked them then, and I'd recommend them now - I found the selections from Xenophon and Herodotus to be fascinating glimpses of ancient life. These men may have been "historians", but the selections in Wilding about keeping mosquitoes off you by building platforms on stilts and using fishing nets (Herodotus), or dwelling underground and keeping animals like goats and sheep in your cave-dwelling (Xenophon), are humanism more than they are history. After that I studied Classics and did some post-graduate Greek in 2004 and have since read Plato's Republic in the original, so these books can't have been a bad introduction to the subject. Other books I used were Deigma, and Teach Yourself Greek by Gavin Betts.
(No-one has yet mentioned that this book only looks at one of the verb conjugations, the "-o" conjugation. There is also the "-mi" conjugation which will have to be learnt, but it's not the case that this book is ripping you off by only giving you part of the picture - it's a beginners book!
Appended following Davey Jones's comment:
In case there's any confusion, Wilding explicitly wrote his book for use in conjunction with Abbott and Mansfield's Greek Grammar, so you should purchase both books together. Some find A&M will last them all their lives (I knew a 60-year-old Classics graduate who never used anything else). I personally don't ever bother with English to Greek exercises. I don't remember the lack of a key to be a problem, but it was 12 years ago. It depends on the learner. I'm comfortable without a Greek to English key. I know when I feel that I understand something, and then I progress on to the next section, but any such book as this I read at least three times, and getting to the end of the book is a good way to appreciate the early contents better the next time you read it. My belief is that the key to learning a language is the vocab - just keep hammering away memorising that and everything will become clear.