1. Theories and Models: a Philosophical Overview -- 2. Thermostatics -- 3. Kinetic Theory of Gases -- 4. Classical Probability -- 5. Modern Probability: Syntax and Models -- 6. Modern Probability: Competing Semantics -- 7. Setting-up the Ergodic Problem -- 8. Models and Ergodic Hierarchy -- 9. Ergodicity vs. Integrability -- 10. The Gibbs Canonical Ensembles -- 11. Phase Transitions: van der Waals to Lenz -- 12. Ising and Related Models -- 13. Scaling and Renormalization -- 14. Quantum Models for Phase Transitions -- 15. Approach to Equilibrium in Quantum Mechanics -- 16. The Philosophical Horizon -- A. Appendix: Models in Mathematical Logic -- A.1 Syntax -- A.2 Semantics -- B. Appendix: The Calculus of Differentials -- B.1 Green's Theorem -- B.2 Stokes' and Gauss' Theorems -- B.3 Higher Differentials -- C. Appendix: Recursive Functions -- D. Appendix: Topological Essences -- D.1 Basic Definitions -- D.2 Examples from Functional Analysis -- D.3 Separability and Compactness -- D.4 The Baire Essentials -- E. Appendix: Models vs. Models -- E.1 Models in Wigner's Writings and in the Third Wigner Symposium -- E.2 A Search for Precedents -- E.3 The Case -- E.4 Closing Statements -- References -- Citation Index.