I've heard a lot of criticism on this work: that is is confusing, jumbled, and out dated. But I personally have found it helpful in my studies, and enjoyable to read. However, for someone very new to the subject of the Celts, I'd recommend "Exploring the World of the Celts" by Simon James, instead.
The book is fairly comprehensive, commenting on the many sub-groups of the peoples contained in the word "Celtic". But herein lies the biggest flaw, in my opinion. It is all very well to recognize the Gauls, Galatians, Welsh, and Picts as Celtic, but there are differences in these groups that may have been overlooked too casualy in Chadwick's work. I've learned all too well, in the process of my own studies, that we cannot correctly assess certain characteristics as generally Celtic, nor can we judge one sub-group of the Celts by another. To do so is simply incorrect. We may make educated assumptions about the social structure of the Britons based on, for example, recorded i nformation from from Gaul, but this will not neccisarily be true. We can't assume that all Celts fought in mortal combat at feasts because Posedonius tells us that is a practice of the Gauls. And I think that this type of assessment is too common in Chadwick's work. Nevertheless, because I'm capable of picking instances like these out, for the most part, I wasn't hampered by the work.
Anothe criticism of this book is that it is fairly unorganized. One paragraph may be talking about the Dalriadic Scots and next about the Welsh under Roman rule. In this sense, I wasn't able to use the book much for quick references, and I found myself knee-deep in only somewhat relevent information when looking for specific information.
My last criticism of The Celts is the near total lack of citations and explanitory footnotes. I'm not fond of taking information on the author's word alone. Although, I suppose this is a fualt rather in the dating of the book, typical of other works put out in the same age. That does not excuse the many times I came to be asking myself about the source of the information Chadwick had given.
Despite my criticisms I did find the book enjoyable, easy to read, and helpful. It is more the type of book I'd pick up to read to brush up, rather than the type of book I'd pick up for reference or for details on a specific subject. The most thourough and well explained chapter in the book seems to be "The Celts in Europe". The intro by Barry Cunliff was also a nice addition.