This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Numerical Methods and Applications, NMA 2018, held in Borovets, Bulgaria, in August 2018. The 56 revised regular papers presented were carefully reviewed and selected from 61 submissions for inclusion in this book. The papers are organized in the following topicalsections: numerical search and optimization; problem-driven numerical method: motivation and application, numerical methods for fractional diffusion problems; orthogonal polynomials and numerical quadratures; and Monte Carlo and Quasi-Monte Carlo methods.