Good book for already knowlegeable reader
This is great book for someone who knows elasticity and some continuum mechanics. recommended for graduate students who will pursue research requiring nonlinear elasticity. For average course on elasticity, this might not be the best book.

A defense of Ogden
It is easy to see why other reviewers do not like this book: it is very advanced. It is not for an undergraduate, and probably not for a graduate student unless she or he is already very familiar with elasticity and solid mechanics. It is not, at bottom, a text for learning the rudiments of the theory of elasticity: it is more on the level of a research monograph, and Malvern or Fung are better choices for many students. However, Ogden is probably the best work available (other than perhaps Truesdell, who can be an acquired taste) on the rigourous theory of non-linear elasticity. If you have an interest in the structure of constitutive relations, need a rigourous mathematical reference for finite element modeling, or are interested in exploring the assumptions and limitations of the linearised theory of elasticity, Ogden is not just the best place to start, but possibly the only place to go.

If you can't teach it, you don't understand it.
This is a horribly written book. Instead of teaching non-linear elasticity to the reader, Ogden hides behind jargon and notation. Perhaps if you know finite elasticity very well, it would serve as a good reference.

If you are interested in learning continuum mechanics, I recommend starting with Introduction to the Mechanics of a Continuous Medium, by L. E. Malvern. Then continue with Nonlinear Solid Mechanics: A Continuum Approach for Engineers, by G. A. Holzapfel.

Not good.
I have a big problem with the Dover series to which this book belongs. The price may look good, but explanations are brief and visual representations of subjects treated are sparse. Don't buy this book.