QCD, the theory of strong interactions, has been defined as our most perfect physical theory, in part because its compact and apparently simple Lagrangian hides a plethora of emerging phenomena. The aim of the present project is to make the essential contributions to fully exploit the new possibilities of the Large Hadron Collider to characterise unexplored domains of QCD.Three main working plans are foreseen: i) The partonic structure of the protons and nuclei at LHC energies, where I plan to unravel the structure at small fraction of momentum of the colliding objects, characterising new regimes of QCD at high parton densities; ii) A new theory of jets in a medium, in which a new way of understanding the phenomenon of parton branching of a quark or gluon in a medium, including new evolution equations is proposed; iii) A Monte Carlo for jet quenching, where the solid theoretical framework developed in the previous point will be implemented into a Monte Carlo code for general use. Along these working plans, two horizontal lines - Talking to the experiment: finding the signatures; and Talking to other fields - will ensure the coherence of the project and the communication of the results as well as the collaboration with external researchers, especially experimentalist.In order to fulfil these ambitious goals, the research team will need of reinforcement in terms of (wo)manpower and travel and computer resources. The total requested contribution from the ERC-StG to the project is 1.499.376 Euros, which is divided as follows: 39% for postdocs; 18% for PhD students; 12% for visits to CERN; 10% for the PI salary; 8% for travel; 8% for computers and 4% for visitors.