These Proceedings of a NATO-ARW (HTECH ARW 96 00 52) held at the International Center for Theoretical Physics, Trieste, Italy from Aug 5 till Aug 9, 1996 resulted from many discussions between various workers, concerning the need for a gathering of all (if possible) who were concerned about the subject of superconductivity fluctuations in High critical Temperature Superconductors (HTS). It appeared to many that the Skocpol-Tinkham work of 1975 had to be revitalized in view of the discovery of the new superconducting ceramics and the enormous amount of work having already taken place. The study of HTS is one of the most prominent research subject in solid state sciences. The understanding of the role of fluctuations is also thought to be necessary before technological applications since the fluctuations may destroy the superconducting state. The workshop discussions have touched upon (i) Superconducting fluctuations in the vicinity of the critical transition, (ii) Superconductivity fluctuations near the percolation transition, and (iii) Fluctuations of the vortex lattice at the lattice melting temperature. These topics served as initiators for a very great amount of discussions with many comments from the audience. More than forty "long lectures" and two "poster sessions" were held. Private discussions going unrecorded but obviously took place at many locations : lecture halls, staircases, cafetaria, bedrooms, bars, beach, . . .

The study of high critical temperature superconductors (HTS) is one of the most prominent research subjects in solid state science. An understanding of the role of fluctuations is also believed to be necessary in advance of technological applications, since the fluctuations may destroy the superconducting state. The discussions focus on: superconducting fluctuations in the vicinity of the critical transitions; superconductivity fluctuations near the percolation transition; and fluctuations of the vortex lattice at the lattice melting temperature. The effects of fluctuations on static properties and on electrical and thermal transport, properties in the ab plane and along the c axis, the effect of a magnetic field on phenomena, specifically in layered compounds are still undecided. The effect of a magnetic field is still not clear. Specific fluctuations of the vortex lattice in HTS ceramics as compared to conventional superconductors are still intensely debated.