2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61066We develop the theory of multiple polylogarithms from analytic, Hodge and motivic point of view. Define the category of mixed Tate motives over a ring of integers in a number field. Describe explicitly the multiple polylogarithm Hopf algebra.82 pages, LATEX, exposition slightly improved, misprints corrected. No major changesAlgebraic GeometryNumber Theory14F42text