Statistical Mechanics is the study of systems where the number of interacting particles becomes infinite. In the last 50 years tremendous advances have been made which have required the invention of entirely new fields of mathematics such as quantum groups and affine Lie algebras; have made remarkable discoveries concerning non-linear differential equations and algebraic geometry; and have produced profound insights in both condensed matter physics and quantum field theory. This book sets out to make all these advances accessible to a readership of graduate and higher level researchers.

1. Basic Principles 2. Reductionism, Phenomena and Models 3. Stability, Existence and Uniqueness 4. Theorems on Order 5. Critical Phenomena and Scaling Theory 6. Mayer Virial Expansions and Groenevelt's Theorems 7. Ree-Hoover Virial Expansion and Hard Spheres 8. High Density Expansions 9. High Temperature Expansions for Magnets at H=0 10. The Ising Model in Two Dimensions; Summary of Results 11. The Pfaffian Solution of the Ising Model 12. Ising Model Spontaneous Magnetization, Form Factors and Susceptibility 13. The Star-Triangle (Yang-Baxter) Equation 14. The Eight Vertex and XYZ models 15. The RSOS and the Chiral Potts models 16. Conclusion

Barry M McCoy , Institute for Theoretical Physics, State University of New York, Stony Brook