"Symbiosis is described as a close relationship between different biological species. It is a pervasive phenomenon, often of a long term nature. It has been estimated that 50% of all known species are parasites, i.e. maintain a symbiotic relation with another species from which they benefit while the partner in the relation is harmed, and that close to a 100% of all plants and animals are parasitised as individuals. Indeed, there are thought to be 10 times more bacterial cells in a human body than human cells. There is growing recognition that symbiosis has a profound impact on the origin and maintenance of the biome and of its ecosystems, on the health of living organisms, and even on sex! Symbiosis thus appears essential to understand some of the most fundamental evolutionary and functional questions related to living organisms. Nevertheless, although symbiotic relationships have been studied by biologists since the early 19th century, they remain little explored by computational biologists. Yet, investigating the enormous variety of such relationships raises formidable mathematical and computational issues. By a highly pluri-disciplinary approach that blends mathematics, algorithmics and wet-lab experiments, we propose to do an intensive, large-scale exploration of the huge variety of genomic and biochemical landscapes observed in the symbiont world, at the interface between symbionts and hosts, and of both with their environment. Our objective is to arrive at a clear view of the importance of symbiosis. This could have far-fetched theoretical and practical implications, notably on our notions of health, our relation with our environment, and our idea of what is species identity, including our idea of what is an individual ."