The book "Meshfree Methods for Partial Differential Equations III" provides a comprehensive overview of the latest developments in the application of meshfree methods for the numerical solution of partial differential equations. These methods are becoming increasingly important in various fields of application due to their high flexibility and versatility. Engineers, scientists, and mathematicians are drawn to this dynamic research area, which offers innovative approaches to solving complex problems in applied mathematics, physics, and engineering. The volume contains a collection of articles that address different meshfree techniques, their mathematical properties, and practical applications. The contributions come from leading experts in the field and represent the current state of research.