The topic of the book has been recently intensively studied both by physicists and mathematicians. The first explicit idea of the AdS/CFT correspondence was formulated by Maldacena almost ten years ago and it immediately created a strong wave of interest among physicists working in string theory. The reason for that is that it suggests a duality between a theory with quantum gravity in a spacetime and a conformal field theory on its boundary. The same correspondence was used in mathematics for special purposes for two decades already. The meeting organized at IRMA in Strasbourg in 2003 brought together mathematicians and physicists working in quickly expanded field. The book is the proceedings of the conference. On mathematical side, there are by M. T. Andersen (a review of geometrical aspects), by R. Graham and K. Hirachi (obstruction tensor and Q-curvature), M. T. Anderson, P.T. Chrusciel and E. Delay (new static solutions of Einstein equations in higher dimensions), Ch. Frances (a construction of AdS/CFT spacetimes) and M. Herzlich (a concept of mass for asymptotical hyperbolic manifolds). The contributions coming from string theory side are written by J. de Boer, L. Maoz and A. Naqvi (a review of some aspects of the correspondence in physics), I. Papadimitriou and K. Skenderis (a Hamiltonian approach to holographic renormalization), S. N. Solodukhin (holographic description for Minkowski space) and J. P. Gauntlett, D. Martelli J. Sparks and D. Waldram (supersymmetric AdS5 solutions of M-theory). The book brings recent results covering many different parts of the AdS/CFT correspondence, it is a very useful addition to the literature both for mathematicians and physicists interested in the field.

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