2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157332These notes contain results concerning uniform exponential growth which were obtained in collaborations with E. Breuillard and A. Salehi-Golsefidy, mostly during 2005, improving Eskin-Mozes-Oh theorem \cite{EMO}, as well as a uniform uniform version of Tits alternative improving \cite{uti}.Group Theorytext