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This text has two goals. The first is to give an introduction to Ecalle'swork on mould theory, multiple zeta values and double shuffle theory and relatethis work explicitly to the classical theory of multiple zeta values and doubleshuffle expressed in the usual terms of non-commutative variables. The secondis to provide complete proofs of those of his main results and identities whichare strictly useful in the context of (non-colored) multiple zeta values. Manyof these proofs are difficult, laborious and not enlightening and have beenrelegated to appendices. The emphasis in the text is to provide an easilyapproachable introduction to Ecalle's language while placing it almost from thestart in the context of multiple zeta value theory.  Disclaimer: This text is not final and is not submitted for publication. Theintention is to continue to add to and complete it over time.

ARI, GARI, Zig and Zag: An introduction to Ecalle's theory of multiple zeta values