1. General theory of eigenstrains.- 1. Definition of eigenstrains.- 2. Fundamental equations of elasticity.- 3. General expressions of elastic fields for given eigenstrain distributions.- 4. Exercises of general formulae.- 5. Static Green's functions.- 6. Inclusions and inhomogeneities.- 7. Dislocations.- 8. Dynamic solutions.- 9. Dynamic Green's functions.- 10. Incompatibility.- 2. Isotropic inclusions.- 11. Eshelby's solution.- 12. Ellipsoidal inclusions with polynomial eigenstrains.- 13. Energies of inclusions.- 14. Cuboidal inclusions.- 15. Inclusions in a half space.- 3. Anisotropic inclusions.- 16. Elastic field of an ellipsoidal inclusion.- 17. Formulae for interior points.- 18. Formulae for exterior points.- 19. Ellipsoidal inclusions with polynomial eigenstrains in anisotropic media.- 20. Harmonic eigenstrains.- 4. Ellipsoidal inhomogeneities.- 22. Equivalent inclusion method.- 23. Numerical calculations.- 24. Impotent eigenstrains.- 25. Energies of inhomogeneities.- 26. Precipitates and martensites.- 5. Cracks.- 27. Critical stresses of crakes in isotropic media.- 28. Critical stresses of cracks in anisotropic media.- 29. Stress intensity factor for a flat ellipsoidal crack.- 30. Stress intensity factor for a slit-like crack.- 31. Stress concentration factors.- 32. Dugdale-Barenblatt cracks.- 33. Stress intensity factor for an arbitrarily shaped plane crack.- 34. Crack growth.- 6. Dislocations.- 35. Displacement fields.- 36. Stress fields.- 37. Dislocation density tensor.- 38. Dislocation flux tensor.- 39. Energies and forces.- 40. Plasticity.- 41. Dislocation model for fatigue crack initiation.- 7. Material properties and related topics.- 42. Macroscopic average.- Random distribution of inclusions-Mori and Tanaka's theory.- 43. Work-hardening ofdispersion hardened alloys.- 44. Diffusional relaxation of internal and external stresses.- 45. Average elastic moduli of composite materials.- 46. Plastic behavior of polycrystalline metals and composites.- 47. Viscoelasticity of composite materials.- 48. Elastic wave scattering.- 49. Interaction between dislocations and inclusions.- 50. Eigenstrains in lattice theory.- 51. Sliding inclusions.- 52. Recent developments.- Appendix 1.- Einstein summation convention.- Kronecker delta.- Permutation tensor.- Appendix 2.- The elastic moduli for isotropic materials.- Appendix 3.- Fourier series and integrals.- Dirac's delta function and Heaviside's step function.- Laplace transform.- Appendix 4.- Dislocations pile-up.- References.- Author index.