This is a new, completely revised, updated and enlarged edition of the
author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for
Mathematicians" in two volumes (this is the 2nd volume). In the
eighties, a group of theoretical physicists introduced several models
for certain disordered systems, called "spin glasses". These models are
simple and rather canonical random structures, of considerable interest
for several branches of science (statistical physics, neural networks
and computer science). The physicists studied them by non-rigorous
methods and predicted spectacular behaviors. This book introduces in a
rigorous manner this exciting new area to the mathematically minded
reader. It requires no knowledge whatsoever of any physics. The present
Volume II contains a considerable amount of new material, in particular
all the fundamental low-temperature results obtained after the
publication of the first edition.