the many different applications that this theory provides. We mention
that the existing literature on this subject includes the books of J. P.
Aubin, J. P. Aubin-A. Cellina, J. P. Aubin-H. Frankowska, C. Castaing-M.
Valadier, K. Deimling, M. Kisielewicz and E. Klein-A. Thompson. However,
these books either deal with one particular domain of the subject or
present primarily the finite dimensional aspects of the theory. In this
volume, we have tried very hard to give a much more complete picture of
the subject, to include some important new developments that occurred in
recent years and a detailed bibliography. Although the presentation of
the subject requires some knowledge in various areas of mathematical
analysis, we have deliberately made this book more or less
self-contained, with the help of an extended appendix in which we have
gathered several basic notions and results from topology, measure theory
and nonlinear functional analysis. In this volume we present the theory
of the subject, while in the second volume we will discuss mainly
applications. This volume is divided into eight chapters. The flow of
chapters follows more or less the historical development of the subject.
We start with the topological theory, followed by the measurability
study of multifunctions. Chapter 3 deals with the theory of monotone and
accretive operators. The closely related topics of the degree theory and
fixed points of multifunctions are presented in Chapters 4 and 5,
respectively.
