Preface -- Table of Contents -- Deformation quantization, methods and applications -- Deformation quantization: genesis, developments and metamorphoses -- Deformation quantization of covariant fields -- On the trace density in deformation quantization -- Deformed double Yangians and quasi-Hopf algebras -- On the representation theory of deformation quantization -- Unimodular vector fields and deformation quantization -- Harrison cohomology and abelian deformation quantization on algebraic varieties -- Related semi-classical and Toeplitz algebras -- Fedosov connections on jet bundles and deformation quantization -- Quantization of Lie bialgebras via the formality of the operad of little disks.