The Editors are delighted to welcome this contribution from a venerable pioneer of algorithmic composition who is also a member of Organised Sound’s Advisory Board. In this article, edited from notes for a series of lectures delivered in Poland, and not previously published, Xenakis tackles first the questions arising from determinacy and indeterminacy, repetition and variation, symmetry and structure, and multidimensional musical space. He later describes his computer drawing interface, UPIC, and ends with a discussion of some of his statistical compositional methods employing a variety of probability distributions. Much of the article is illuminated by insights drawn from a lifetime’s work in the arts and sciences.