The study of disorder has generated enormous research activity in mathematics
and physics. Over the past 15 years various aspects of the subject have changed
a number of paradigms and have inspired the discovery of deep mathematical
techniques to deal with complex problems arising from the effects of disorder.
One important effect is a phenomenon called localization, which describes the
very strange behavior of waves in random media---the fact that waves, instead of
traveling through space as they do in ordered environments, stay in a confined
region (caught by disorder). To date, there is no treatment of this subject in
monograph or textbook form. This book fills