1. Introduction and Guide to This Text.- 2. Statistical Thermodynamics.- 2.1 Spins in a Magnetic Field.- 2.2 The Partition Function.- 2.3 The Concept of the Molecular Field.- 2.4 Discontinuity in Specific Heat.- 2.5 Magnetic Susceptibility and Spontaneous Magnetization.- 2.6 Antiferromagnetism.- 2.7 Short-Ranged Versus Long-Ranged Interactions.- 2.8 Fermions, Bosons, and All That.- 2.9 Gaussian and Spherical Models.- 2.10 Magnetic Susceptibility in Gaussian and Spherical Models.- 2.11 Spherical Antiferromagnet.- 2.12 Spherical Model Spin Glass.- 2.13 Magnetic Properties of Spin Glass.- 2.14 Thermodynamics of Magnons.- 2.15 Magnetism in Two Dimensions.- 2.16 The XY Mode1:1D.- 2.17 The XY Model:2D.- 2.18 Transfer Matrix of Plane Rotator Model.- 3. The Ising Model.- 3.1 High Temperature Expansions.- 3.2 Graph Theory.- 3.3 Low Temperature Expansions and the Duality Relations.- 3.4 Peierls’ Proof of Long Range Order.- 3.5 1D Ising Model in Longitudinal Fields.- 3.6 1D Ising Model in Transverse Fields.- 3.7 Concerning Quadratic Forms of Fermion Operators.- 3.8 Two-Dimensional Ising Model: The Transfer Matrix.- 3.9 Solution of Two-Dimensional Ising Model in Zero Field.- 3.10 Spontaneous Magnetization and Magnetic Susceptibility.- 3.11 Zeros of the Partition Function.- 3.12 Miscellania, Including 2D Antiferromagnets.- 3.13 The Three-Dimensional Ising Model.- References.- List of Tables.- Errata for The Theory of Magnetism I (Springer Series in Solid-State Sciences, Vol. 17).

It is here that the systematic study of magnetic materials has provided one of the best ways of examining this question, which is one of the principal concerns of statistical physics (alias "statistical mechanics") and of modern thermodynamics.