1 Crystals 1.1 Periodicity of Crystal Structure, Crystal Cell 1.2 Three-Dimensional Lattice Types 1.3 Symmetry and Point Groups 1.4 Reciprocal Lattice 1.5 Appendix of Chapter 1: Some Basic Concepts 1.5.1 Concept of Phonon 1.5.2 Incommensurate Crystals 1.5.3 Glassy Structure 1.5.4 Mathematical Aspect of Group References2 Framework of Crystal Elasticity 2.1 Review on Some Basic Concepts 2.1.1 Vector 2.1.2 Coordinate Frame 2.1.3 Coordinate Transformation 2.1.4 Tensor 2.1.5 Algebraic Operation of Tensor 2.2 Basic Assumptions of Theory of Elasticity 2.3 Displacement and Deformation 2.4 Stress Analysis 2.5 Generalized Hooke's Law 2.6 Elastodynamics, Wave Motion 2.7 Summary References3 Quasierystal and Its Properties 3.1 Discovery of Quasicrystal 3.2 Structure and Symmetry of Quasicrystals 3.3 A Brief Introduction on Physical Properties of Quasicrystals 3.4 One-, Two- and Three-Dimensional Quasicrystals 3.5 Two-Dimensional Quasicrystals and Planar Quasicrystals References4 The Physical Basis of Elasticity of Solid Quasicrystals 4.1 Physical Basis of Elasticity of Quasicrystals 4.2 Deformation Tensors 4.3 Stress Tensors and Equations of Motion 4.4 Free Energy Density and Elastic Constants 4.5 Generalized Hooke's Law 4.6 Boundary Conditions and Initial Conditions 4.7 A Brief Introduction on Relevant Material Constants of Solid Quasicrystals 4.8 Summary and Mathematical Solvability of Boundary Value or Initial-Boundary Value Problem 4.9 Appendix of Chapter 4: Description on Physical Basis of Elasticity of Quasicrystals Based on the Landau Density Wave Theory References5 Elasticity Theory of One-Dimensional Quasicrystals and Simplification 5.1 Elasticity of Hexagonal Quasicrystals 5.2 Decomposition of the Elasticity into a Superposition of Plane and Anti-plane Elasticity 5.3 Elasticity of Monoclinic Quasicrystals 5.4 Elasticity of Orthorhombic Quasicrystals 5.5 Tetragonal Quasicrystals 5.6 The Space Elasticity of Hexagonal Quasicrystals 5.7 Other Results of Elasticity of One-Dimensional Quasicrystals References6 Elasticity of Two-Dimensional Quasicrystals and Simplification.. 6.1 Basic Equations of Plane Elasticity of Two-Dimensional Quasicrystals: Point Groups 5m and lOmm in Five and Tenfold Symmetries 6.2 Simplification of the Basic Equation Set: Displacement Potential Function Method 6.3 Simplification of Basic Equations Set: Stress Potential Function Method 6.4 Plane Elasticity of Point Group 5, 5 and 10, 1--0 Pentagonal and Decagonal Quasicrystals 6.5 Plane Elasticity of Point Group 12mm of Dodecagonal Quasicrystals References7 Application I--Some Dislocation and Interface Problems and Solutions in One and Two Dimensional Quasicrystals ���� 8 Application H--Solutions of Notch and Crack Problems of One and Two Dimensional Quasicrystais9 Theory of Elasticity of Three-Dimensional Quasicrystals and Its Applications10 Phonon-Phason Dynamics and Defect Dynamics of Solid Quasicrystals11 Complex Analysis Method for Elasticity of Quasicrystals12 Variational Principle of Elasticity of Quasicrystals, Numerical Analysis and Applications13 Some Mathematical Principles on Solutions of Elasticity of Quasicrystals14 Nonlinear Behaviour of Quasicrystals15 Fracture Theory of Solid Quasicrystals16 Hydrodynamics of Solid Quasicrystals17 Remarkable ConclusionMajor Appendix: On Some Mathematical Additional Materials