2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158242We give a brief exposition on the uses of non-commutative fundamental groups for the study of Diophantine problems via a non-abelian Albanese map.Expository article based on colloquium lecture at LeedsAlgebraic GeometryNumber Theory14G25Fundamental groups and Diophantine geometrytext