The AdS/CFT relation, quasi-normal modes and applications

Here we present a fast review of some of developments and new results concerning applications of gravity in the context of the AdS/CFT correspondence, in brane world perturbations as well as in holographic superconductors. We also discuss the structure of the phase transitions in a more general set up defined by the quasi-normal oscillations in the bulk, which signalize a very complex structure of the phase transition at the border.