This is the third workshop on moment method in kinetic theory. The first and the second very successful workshops are the workshop on "Moment Methods in Kinetic Gas Theory" that was held hosted at the Eidgen össische Technische Hochschule (ETH) in Zürich, Switzerland from November 6-8, 2008, and the workshop on "Moment Methods in Kinetic Theory II" that was held at the Fields Institute, University of Torento, Canada from October 14-17, 2014. We will try to bring together leading researchers, mathematicians, scientist, and engineers, at all academic levels, involved in the theory, development, application, and solution of moment closures arising from kinetic theories. Researchers involved in direct solution of kinetic descriptions will also participate. The workshop will focus on recent advances in the mathematical theory of moment closures, advanced numerical solution methods for their solution, and the application and evaluation of moment method techniques for a range of problems, including new applications in social sciences and biology.