The book is based on the lecture course "Function spaces", which the
author gave for more than 10 years in the People's Friendship University
of Russia (Moscow). The idea to write this book was proposed by
Professors H. Triebel and H.-J. SchmeiBer in May-June 1993, when the
author gave a short lecture course for post-graduate students in the
Friedrich-Schiller University Jena. The initial plan to write a short
book for post-graduate students was trans- formed to wider aims after
the work on the book had started. Finally, the book is intended both for
graduate and post-graduate students and for researchers, who are
interested in applying the theory of Sobolev spaces. Moreover, the
methods used in the book allow us to include, in a natural way, some
recent results, which have been published only in journals. Nowadays
there exist numerous variants and generalizations of Sobolev spaces and
it is clear that this variety is inevitable since different problems in
real analysis and partial differential equations give rise to different
spaces of Sobolev type. However, it is more or less clear that an
attempt to develop a theory, which includes all these spaces, would not
be effective. On the other hand, the basic ideas of the investigation of
such spaces have very much in common.