This is a new, completely revised, updated and enlarged edition of the
author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for
Mathematicians". This new edition will appear in two volumes, the
present first volume presents the basic results and methods, the second
volume is expected to appear in 2011. 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 first volume of
this new and completely rewritten edition presents six fundamental
models and the basic techniques to study them.