Part I. The Mathematical Foundations of Finite Strain Theory: 1. Introduction; 2. Mathematical description of homogeneous deformations; 3. Infinitesimal deformation; 4. Transformations describing deformations of a material medium; 5. Forces; 6. Boundary conditions and work; 7. Another unique factorisation of D; 8. Virtual work; 9. Transformation of cartesian tensors; Part II. Non-Hydrostatic Thermodynamics: 10. The thermodynamic basis; 11. Thermodynamic relations; 12. Thermodynamic functions, equations of state; 13. Thermodynamic quantities, definitions, and geometrical situation; 14. Thermal expansion coefficients; 15. Specific heats; 16. Elastic stiffness and compliances; 17. Tensorial forms for the elastic stiffness and compliance matrices; 18. The effects of symmetry on the thermodynamic properties of crystals; 19. Equilibrium and stability conditions for thermodynamic systems; 20. Equilibrium conditions for diffusion in phases under non-hydrostatic stresses; 21. The equilibrium of a stressed solid in contact with a solution of the solid; 22. The thermodynamic stability of a phase; 23. Discussion of the elastic stability conditions; 24. Phase transitions and instability; 25. An example of a phase transition involving a simple shear; 26. Limiting the values of thermodynamic quantities at an instability; 27. The a-ß quartz transition; 28. The thermodynamic theory of the growth of Dauphiné twinning in quartz under stress; 29. The tetragonal/cubic ferroelectric transition of barium titanate; References; Index.