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Ch. 1. Preliminaries. 1.1. Basic equations for solid mechanics. 1.2. Numerical techniques: FEM vs. S-PIM. 1.3. Basic ideas of S-PIM. 1.4. Basic properties of S-PIM. 1.5. Basic steps in S-PIM. 1.6. Basic settings in S-PIM. 1.7. Outline of the book. 1.8. References -- ch. 2. G spaces. 2.1. General issues on function spaces. 2.2. Useful spaces in weak formulation. 2.3. G spaces: definition. 2.4. [symbol] space: basic properties. 2.5. [symbol] space: other properties. 2.6. Concluding remarks. 2.7. References -- ch. 3. PIM shape function creation. 3.1. Requirements on shape functions. 3.2. PIM shape functions. 3.3. RPIM shape functions. 3.4. PIM-CT shape functions. 3.5. Isoparametric PIM shape functions. 3.6. Alpha PIM shape functions. 3.7. Condensed RPIM shape functions. 3.8. Other methods. 3.9 Interpolation error estimation. 3.10. Concluding remarks. 3.11. References -- ch. 4. Strain field construction. 4.1. Why constructing strain field? 4.2. Discrete models: a base for strain construction. 4.3. General procedure for strain construction. 4.4. Admissible conditions for constructed strain field. 4.5. Strain construction techniques. 4.6. A brief historical note. 4.7. Concluding remarks. 4.8. References -- ch. 5. Weak and weakened weak formulations. 5.1. Briefing on weak forms. 5.2. Galerkin weak form. 5.3. Galerkin weak forms: alternative expressions. 5.4. FEM: a typical Galerkin weak formulation. 5.5. SC-Galerkin: a general W[symbol] formulation. 5.6. GS-Galerkin: a widely used W[symbol] form. 5.7. S-PIM: a typical W[symbol] formulation. 5.8. Error assessment in S-PIM and FEM models. 5.9. Concluding remarks. 5.10. References -- ch. 6. Node-based smoothed point interpolation method (NS-PIM). 6.1. NS-PIM for 2D solids. 6.2. NS-RPIM for 2D solids. 6.3. NS-PIM/NS-RPIM for 3D solids. 6.4. Upper bound properties of NS-PIM/NS-RPIM. 6.5. Concluding remarks. 6.6. Computer program. 6.7. References