The International School for Advanced Studies in Trieste offers 2 fellowships in the framework of an "Advanced Training Programme"" leading to a fast track PhD in connection with the Inter-University Master course in Physics jointly delivered by the Universities of Trieste and Udine. The programme lasts 2 years, it is aimed to candidates who wish to acquire theoretical tools and necessary skills to start a high level research activity in Theoretical Physics of the Condensed Matter and it consists of two parallel and complementary trainings: the Inter-University Master course in Physics jointly delivered by the Universities of Trieste and Udine and a set of courses held by the researchers and professors of the SISSA Theory and Numerical Simulations of the Condensed Matter PhD course.