This book provides a mathematically rigorous introduction to the theory of elasticity. This book is excellent for pure/applied mathematicians with background in differential geometry and functional analysis interested in learning the basics of elasticity. Before I found this book I tried to learn some elasticity theory from many other books, however the biggest obstruction was always the lack of clarity in the mathematical formulation. Most of the books dealing with theory elasticity do not provide clear definitions of basic mathematical concepts they use throughout the book, as a consequence this produces a very informal exposition difficult to reconciliate with the usual concepts in differential geometry. Marsden & Hughes' book fill this gap in the literature giving a rigorous mathematical exposition easily understandable by any math student with background in differential geometry.
Courses in theory of elasticity are very common in the core curriculum of mathematics programs at Russian universities. There are dozens of excellent textbooks in Russian aimed at mathematics students, however as I mentioned before, in the English literature this is the first book, as far as I know, that provides such a mathematical presentation of the subject. I really recommend this book to any pure/applied math student looking for a good introduction to elasticity with the same language and mathematical rigour as we are used to.
On the other hand, I would say that this book is not very suitable for engineering students (at the level of universities/colleges in North America), however they have plenty of books where they can learn elasticity from the applied or computational point of view.
Sb. said this book turns 1+1=2 into a nightmare, however I can't agree. First, this book is not written for engineers. For engineers, there are a dozen of good elasticity books, eg. the classics Fung's "Foundation of solid mechanics". This is not the right book for engineers. This book deals elasticity within the context of manifold. For these of you who really want to know what a tensor really is, what the real meaning of these 1+1=2, for example C=F'F, in the general settings, this is the right one. As it is said, knowing elasticity, finite deformation theory, nonelasticity is still not enough to open this book. All you need to know is a lot of differential geometry and tensor calculus. This book also try to build up these notions. Good concurrent books to help you understand are "tensor calculus on manifold" by Bishop et. al, and "the geometry of physics" by Frankel. Overall, this is a book very hard to penetrate, and only intended for the advanced level. You won't expect to learn any elasticity from this book if you are new to elasticity. I recommend you to return back to this classic when you think you are ready, you will find a whole new world.
Though I'm a engineer in practice I bought this book out of personal interest to further my knowlegde. When I first opened the book I was a taken aback by the amount of mathematics used. Having a good knowledge of the classical theory of elasticity and some non-linear theory is simply not enough to begin with this book. Know your mathemactics! (differential geometry,etc.) Appart form the starting difficulies the book has very much to offer and is well written. I especially liked the "exotic" topics like relativistic elasticity and bifurcation theory of beams and plates. This book is very different compared to the books I used to read on elasticity but I still enjoy it.
Turning simple problem into nightmare. How difficult can an elasticity problem be in engineering? But these guys just have a way to make 1+1=2 looks like the most mysterious problem mankind has ever come across. No wonder everyone hates engineering and physics nowadays.