I. Mathematical, Physical and Numerical Considerations -- 1. Particle Modeling: What It Is and What It Is Not -- 2. Numerical Methodology -- II. Qualitative Newtonian Modeling -- 3. Elastic Strings and Solitons -- 4. Elastic Snap Through -- 5. Minimal Surfaces -- 6. Biological Self Reorganization -- 7. Cavity Flow -- 8. Turbulent and Nonturbulent Vortices -- 9. Liquid Drop Formation, Fall, and Collision -- 10. Conservative Motion of Tops and Gyroscopes -- III. Quantitative Modeling -- 11. Stress Wave Propagation in Slender Bars -- 12. Colliding Microdrops of Water -- 13. Crack Development in a Stressed Copper Plate -- 14. Liquid Drop Formation on a Solid Surface -- 15. Fluid Bubbles and Jiggling Gels -- 16. Melting Points -- 17. Special Relativistic Motion -- 18. A Speculative Model of the Diatomic Molecular Bond -- References and Sources for Further Reading -- Appendices - FORTRAN Programs and Related Formulas -- A1. Stress. For -- A2. Drop. For -- A3. Morse. For -- A4. Ghexa. For -- A5. Newtonian Iteration Formulas.