Since the discovery in 1986 of high temperature superconductors by J. G. Bednorz and K. A. Muller, a considerable progress has been made and several important scientific problems have emerged. Within this NATO Advanced Study Institute our intention was to focus mainly on the controversial topic of the symmetry of the superconducting gap and given the very short coherence length, the role of fluctuations. The Institute on 'The Gap Symmetry and Fluctuations in High- Superconductors' took place in the "Institut d'Etudes Scientifiques de Cargese" in Corsica, France, between 1 - 13 September 1997. The 110 participantsfrom 18 countries (yet 30 nationalities) including 23 full time lecturers, have spent two memorable weeks in this charming Mediterranean resort. All lecturers were asked to prepare pedagogical papers to clearly present the central physical idea behind specific model or experiment. The better understanding of physics of high temperature superconductivity is certainly needed to guide the development of applications of these materials in high and weak current devices.

This volume contains the proceedings of the 2004 University of Miami Workshop on Unconventional Superconductivity. The workshop was the fourth in a series of successful meetings on High-T Superconductivity and C related topics, which took place at the James L. Knight Physics Building on the University of Miami campus in Coral Gables, Florida, in January 1991, 1995, 1999, and 2004. The workshop consisted of two consecutive events: 1. NATO Advanced Research Workshop (ARW) on New Challenges in Superconductivity: Experimental Advances and Emerging Theories, held on January 11-14, 2004; 2. Symposium on Emerging Mechanisms for High Temperature Superconductivity (SEMHTS), held on January 15-16, 2004. It is hard to write a balanced preface to a volume like this one, yet at least we try to offer the reader a taste of what was happening in this workshop. There were close to a hundred scientists from around the world, albeit fewer Russians than we had originally hoped for. Nevertheless, the workshop was very lively and we trust that this is demonstrated in this volume. The workshop included high-quality presentations on state of the art works, yet a key issue, discussed by many, was how homogeneous the cuprates are. STM data, as well as other reports, showed that the cuprate superconductors (SC's) studied were inhomogeneous, especially in the underdoped regime; while experiments, like ARPES and magnetoresistance have established the existence of a Fermi Surface (FS), at least above some doping level, in the cuprates.