The 3rd edition has an entirely new set of chapters covering asymptotics. I found this to be a very readable survey, including a good discussion of local asymptotic normality, which is not treated in more elementary texts. There's some overlap between this book and Lehman's Theory of Point Estimation. It's not obvious which should be read first, but both books are very well written with many interesting problems.
Lehmann and Romano, Third Edition, fourth printing, 2008, is a wonderful, beautiful, necessary book for the shelf of every serious statistician, but in a few ways it is not quite right. Some important topics are omitted. At least one important topic is much more important than the book says. At least one statement, while correct, may be read incorrectly by beginners. At least one proof is unreadable.An omission is heteroskedasticity. The usual tests for 2-samples and k-samples are wrong in its presence..
This text was commonly used as a graduate text in mathematical statistics in the 1970s when I was a graduate student at Stanford University. It was the best and most detailed text on the theory of hypothesis testing. Over the years it remained so and twenty years after publication, when it was outdated by research advances it was revised by Professor Lehmann. The second edition originally published by Wiley went out of print but has now been reprinted by Springer-Verlag. This is a great book for any statist..