This volume represents the proceedings of the conference on Topics in Deformation Quantization and Non-Commutative Structures held in Mexico City in September 2005. It contains survey papers and original contributions by various experts in the fields of deformation quantization and non-commutative derived algebraic geometry in the interface between mathematics and physics. It also contains an article based on the XI Memorial Lectures given by M. Kontsevich, which were delivered as part of the conference. This is an excellent introductory volume for readers interested in learning about quantization as deformation, Hopf algebras, and Hodge structures in the framework of non-commutative algebraic geometry.
XI Solomon Lefschetz memorial lecture series: Hodge structures in non-commutative geometry (Notes by Ernesto Lupercio) by M. Kontsevich Hopfish structure and modules over irrational rotation algebras by C. Blohmann, X. Tang, and A. Weinstein Deformations and quantizations, an introductory overview by D. Sternheimer SDYM and heavenly equations in deformation quantization by S. Formanski and M. Przanowski On a possible construction of noncommutative topological invariants by O. Obregon, C. Ramirez, and M. Sabido On coherent states for spaces of holomorphic functions related to the hydrogen atom problem in dimensions $n=2,3,5$ by D. Rojas-Sandoval and C. Villegas-Blas Noncommutativity from canonical and noncanonical structures by M. Rosenbaum, J. D. Vergara, and L. R. Juarez Commutative algebras of Toeplitz operators and Berezin quantization by N. Vasilevski.