1. We shall briefly describe the ARI-GARI structure; recall its double origin in Analysis and mould theory; explain what makes it so well-suited to the study of multizetas; and review the most salient results it led to, beginning with the exchanger $adari(pal^\bullet)$ of double symmetries $(\underline{al}/\underline{il}) \leftrightarrow (\underline{al}/\underline{al})$, and culminating in the explicit decomposition of multizetas into a remarkable system of irreducibles, positioned exactly half-way between the two classical multizeta encodings, symmetral resp. symmetrel.

2. Although the coloured, esp. two-coloured, multizetas are in many ways more regular and better-behaved than the plain sort, their sheer numbers soon make them computationally intractable as the total weight $\sum s_i$ increases. But help is at hand: we shall show a conceptual way round this difficulty; make explicit its algebraic implementation; and sketch some of the consequences.

A few corrections and comments about this talk are available in the PDF file at the bottom of the page.[-]