This volume is the proceedings of the online conference 'McKay correspondence, Mutation and Related Topics, ' which was held at Kavli Institute for the Physics and Mathematics of the Universe (IPMU) in Japan in Summer in 2020.This volume consists of 15 peer-reviewed articles written by speakers who lead currently active research fields of McKay correspondence, crepant resolution, singularities, quiver and cluster algebra.The editors believe that this volume is quite useful for all researchers and students who are interested in these fruitful research fields.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North Americ