The notion of space is crucial to Xenakis's music and thought. This chapter will offer a global approach, trying to show the complexity and inner richness of this notion. Indeed, there are at least four levels where we can found it. First, there is the ontological and philosophical level. On that level, space is a fundamental notion for Xenakis. In the 1960s he created the notion of »outside-time structures«, which minimizes the importance of time, and in the 1980s he stated that time could be viewed as an epiphenomenal notion, while space would be more fundamental. On a second level, we could view space as an operative category. The discourse will be about geometric space, and, for instance, the use of graphs for composing music. It is thanks to this kind of space that Xenakis imagined new types of sound morphologies (glissandi, for instance) or that he invented transfers from the microscopic level to the macroscopic. With the third level, we are in the domain of the physical space, where Xenakis was one of the main pioneers, introducing the idea of the »composability« of physical space. It is what happened in the Philips Pavilion of the Brussels World Fair (Expo 58) with the »sound routes«, or with the sound immersion produced with Bohor (1962), or with the metaphor of the »Sonotron« used in Terretektorh (1965-66), etc. With the fourth and final level we can define space as a place where an event occurs: this is the definition of the Xenakian notion of »polytope«.

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