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Iannis Xenakis was a prolific composer who accompanied his work with theoretical writings. Also trained as an engineer, he is known for having used mathematical models in his compositions and for developing a formalization of music. This book presents Xenakis's main theories from an analytical perspective without calling for special knowledge of mathematics. It features numerous musical examples and relies on detailed analyses to explain Xenakis's compositional procedures, yielding new insight into the relation between theory and practice in the composer's music. As a comprehensive study, it also reveals for the first time the extent to which Xenakis borrowed from his earlier works. The use of montage is examined as a compositional device, challenging the view that mathematics plays a dominant role in his music. On the whole, this book offers a fresh approach to the music of Xenakis and contributes to a better understanding of his creative thinking. In the year marking the 10th anniversary of his death, it provides a fitting tribute to one of the most original composers of the twentieth century.