This is an excellent book for those who want to know how poems work. It is primarily concerned with poetry's "nuts and bolts". And it handles that well. If you like Ruth Padel's "52 Poems" and "60 Poems", you will find a lot here to interest you.
When you have read it, it will remain a handy reference for terms used in poetry, for how to punctuate more or less anything, for information on layout and on lineation, for information on syntax, and so on - all in neat sections in the text, easy to find, clearly explained, and all necessary for the appreciation of poetry. The treatment of rhythm and rhyme is basic but good. On criticism and theory the book is a little light, limiting itself to three fairly short chapters, "History", "Biography", and "Gender".
I realise that a single book, even one called "The Poetry Handbook", will not be able to cover everything in depth. For this reason I would recommend that someone new to the study of poetry read alongside it another book to get a fuller picture, something like "Beginning Theory" by Peter Barry or even the "Very Short Introduction to Literary Theory" by Jonathan Culler.
This is not to put down this book at all. I still rate this book at four stars for what it achieves, because it does that very well; and its associated website should remain as useful as the printed text.