2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65294We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff's classification scheme with the connection matrix to define and describe their Galois groups. Then we describe \emph{fundamental subgroups} that give rise to a Riemann-Hilbert correspondence and to a density theorem of Schlesinger's type.Prepublication du Laboratoire Emile Picard n.246. See also http://picard.ups-tlse.frQuantum Algebra05A30 - 12 H 10 - 20 G - 33D - 34M - 39A13text