The book is intended for graduate and post-graduate students and for researchers, especially those who are not specialists in the theory of function spaces and need to use Sobolov spaces as a tool in their investigations. The main concern is with Sobolev spaces defined in domains. The main topics are approximations by infinitely differentiable functions, integral representations, embedding, trace and extension theorems. Contents Preliminaries / Approximation by infitely differentiable functions / Sobolev's integral representation / Embedding theorems / Trace theorems / Extensions theorems / Comments Bibliography / Index