Precambrian stromatolites have received in depth, consideration from geologists and paleontologists; they were indeed searching for biosedimentary structures that were sufficiently characteristic and widely distributed to be considered as useful tools for stratigraphic correlation. Silicified stromatolites are also of interest as they contain preserved traces of ancient life. Calcareous Phanerozoic stromatolites have not received very much attention from geologists. Logan's too schematic morphological classification of 1964, was not so helpful to the knowledge of Phanerozoic stromatolites because neither their morphology nor their microstructure were studied in the same detail in which Proterozoic stromatolites have now been described. We therefore know little about the Phanerozoic stromatolites which, do, however, show an interesting range of diversification. A major questions stiII remaining to be answered include the history of stromatolite development and wether their morphology has "evolved" in addition to detailed information concerning Cenozoic nonmarine stromatolites which precipitate carbonate and the Recent giant stromatolites which trap particles. For these reasons Claude Monty, in 1981, launched the first volume of what was going to be a series on "Phanerozoic stromatolites" in order to describe their morphology, microstructure and paleoecology and to present them in their stratigraphic context.