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This book is a collection of the papers presented at the workshop on 'Symmetry and Heterogeneity in High Tc Superconductors' directed by Antonio Bianconi and Alexander F. Andreev in collaboration with K. Alex Müller and Giorgio Benedek. Philip B. Allen, Neil W. Ashcroft, Alan R. Bishop, J. C. Séamus Davis, Takeshi Egami, Francesco Iachello, David Pines, Shin-ichi Uchida, Subodh R. Shenoy, chaired hot sessione contributing to the success of the workshop. The object of the workshop was the quantum mechanism that allows the macroscopic quantum coherence of a superconducting condensate to resist to the attacks of high temperature. Solution to this problem of fundamental physics is needed for the design of room temperature superconductors, for controlling the decoherence effects in the quantum computers and for the understanding of a possible role of quantum coherence in living matter that is debated today in quantum biophysics. The discussions in the informal and friendly atmosphere of Erice was on new experimental data showing that high T in doped cuprate perovskites is c related with the nanoscale phase separation and the two component scenario, the two-band superconductivity in magnesium diboride and the lower symmetry in the superconducting elements at high pressure.
