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: (i) superconducting fluctuations in the vicinity of the critical transitions; (ii) superconductivity fluctuations near the percolation transition; and (iii) fluctuations of the vortex lattice at the lattice melting temperature. These topics are all the subject of more or less intense debate. 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. In its clear presentation of the experimental, theoretical and simulation aspects, together with the comprehensive list of references, this compendium is the best to appear in over 20 years.