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This reprinted special issue contains all of the articles published in the Special Issue "Advanced Numerical and Computational Methods for Engineering and Applied Mathematical Problems" from the MDPI Mathematics journal. This Special Issue provides a forum for researchers and practitioners to examine topics pertaining to meshfree/particle methods and advanced numerical methods in the domains of engineering and scientific computation. The aim of this Special Issue is to disseminate state-of-the-art fundamental developments for these advanced numerical methods, prospective research directions, and applications for engineering and applied mathematical problems. It is our hope that this Special Issue will make a substantial contribution to research on the theoretical and applied aspects of advanced numerical methods.