The Advanced Summer School was concerned with the introduction to young promising graduate students, advanced undergraduate students  and researchers from Universities abroad the country on the forefront of the main avenues of research in Solid State Physics, Soft Condensed Matter, General Relativity-Gravitation, Particle Physics,  Mathematical Physics, and Medical Physics. The Summer School hosted a series of Lectures presented by world class leaders in each of these fields in the Department of Physics at Cinvestav. Such research lines are also the main interest of the Physics Department which now celebrates its fifty years since its establishment. These proceedings include the review notes of the Lectures as well as plenary talks.