This book provides a comprehensive review of meshless approximation methods, an important alternative to the finite element method, which is widely used for numerical analysis of a wide range of engineering problems. The authors discuss the numerical properties and background information for the most important meshless approximation methods and compare them with the corresponding analytical solutions to verify the accuracy of the results. The text presents complete mathematical formulations and numerical properties, such as convergence, consistency, stability, and adaptivity, in detail. An appendix presents flowcharts to aid programmers in using meshless methods.