2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101320We introduce twisted Alexander norms of a compact connected orientable 3-manifold with first Betti number bigger than one generalizing norms of McMullen and Turaev. We show that twisted Alexander norms give lower bounds on the Thurston norm of a 3-manifold. Using these we completely determine the Thurston norm of many 3-manifolds which can not be determined by norms of McMullen and Turaev.24 pages, accepted for publicaton by the Transactions of the AMSGeometric Topology57M27text