This is a revised and enlarged edition of a book first published in English in 1985. That publication was based on three smaller books in German that had appeared in Teubner's series of texts in mathematics. The book is largely an account of the author's own work on the subject.
In his review of the 1985 edition in the Bulletin of the AMS, Lars Inge Hedberg said that
Generally speaking, this book is not the right choice for someone who is just trying to learn a few simple facts about Sobolev spaces. The author's taste is for completeness. He treats every conceivable aspect of his problems, which makes the book rather overwhelming for the general reader.
Maz'ya's massive book will nevertheless continue to be a fundamental reference for those who work in the field.