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This rigorous introduction to an exciting new research domain is aimed at the mathematically minded and requires no knowledge of any physics. In a new and reworked edition, this first volume presents six fundamental models and the techniques to study them.

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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.

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Introduction.- 1. The Sherrington-Kirkpatrick Model.- 2. The Perceptron Model.- 3. The Shcherbina and Tirozzi Model.- 4. The Hopfield Model.- 5. The V-statistics Model.- 6. The Diluted SK Model and the K-Sat Problem.- 7. An Assignment Problem.- A. Appendix: Elements of Probability Theory.- References.- Index.- Glossary.

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From the reviews:
"It builds stone by stone a remarkable construction, revealing at each step a new piece of the fascinating picture of mean-field spin glass models. ... Enlightening explanations, written with strong commitment, help the reader to grasp the general line of thought before entering into the computations ... . With its depth and proficiency of important techniques, this book opens new perspectives on probability theory and the statistical mechanics of disordered systems. It will be a source of inspiration for generations of mathematicians." (Francis Comets, Mathematical Reviews, Issue 2012 c)

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