Proceedings of the NATO Advanced Research Workshop on Symmetry and Heterogeneity in High Temperature Superconductors, Erice-Sicily, 4-10 October 2003Acknowledgements. Preface.I. Electronic and Exchange-Like Pairing Scenarios.Symmetry and Higher Superconductivity in the Lower Elements; N.W. Ashcroft. Feshbach Shape Resonances in Multiband High Tc Superconductors; A. Bianconi, M. Philippi. Modelling Cuprate Gaps in a Composite Two-Band Model; N. Kristoffel, P. Rubin. Multi-Gap Superconductivity in MgB2; S.P. Kruchinin, H. Nagao.II. Anomalous Electron-Phonon Interaction.Electron-Lattice Coupling in the Cuprates; T. Egami. Symmetry Breaking, Non-Adiabatic Electron-Phonon Coupling and Nuclear Kinetic Effect on Superconductivity of MgB2; P. Banacky.III. Phase Separation and Two Components Cuprates.Microscopic Phase Separation and Two Type of Quasiparticles in Lightly Doped La2-xSrxCuO4 Observed by Electron Paragmagnetic Resonance; A. Shengelaya et al. Phase Separation in Cuprates Induced by Doping, Hydrostatic Pressure or Atomic Substitution; E. Liarokapis. Structural Symmetry, Elastic Compatibility, and the Intrinsic Heterogeneity of Complex Oxides; S.R. Shenoy et al. A Case of Complex Matter: Coexistence of Multiple Phase Separations in Cuprates; G. Campi, A. Bianconi. Anisotropy of the Critical Current Density in High Quality YBa2Cu3O7-d. Thin Film; A. Taoufik et al.IV. Symmetry of the Condensate.Symmetry of High-Tc Superconductors; F. Iachello. Evidence for d-Wave Order Parameter Symmetry in Bi-2212 from Experiments on Interlayer Tunneling; Yu.I. Latyshev.V. Exotic Superconductivity.Electronic State in Co-Oxide Similar to Cuprates? S. Maekawa, W. Koshibae. Oxide Superconductivity; J.D. Dow. Superconductivity Versus Antifererromagnetic SDW Order in the Cuprates and Related Systems; L.S. Mazov.Author Index. Subject Index. Figure Index. Table Index.Key chapters by Neil Ashcroft and K. Alex MuellerNL