The quark confinement mechanism is one of the most difficult problems in particle physics, and is listed as the "7 difficult mathematical problems of the new millennium". The first person who first solves this problem will be awarded a prize of US$1 million by Cray Mathematics Institute. This volume is useful for the systematic understanding of quark confinement and nonperturbative aspects of quantum chromodynamics (QCD) from the wide viewpoints of mathematical physics, lattice QCD physics and quark-hadron physics. It covers the current studies of nonperturbative QCD: quark confinement...