The main objective of this project is to advance the theoretical knowledge on strongly interacting theories in the Standard Model (SM) and beyond (BSM). We will strive for developing new theoretical and computational tools to cast into a coherent fundamental theory existing and forthcoming experimental results from the LHC as well as from many other high-energy experiments. We will conduct our research within the lattice field theory setup. The recent extraordinary theoretical and algorithmic advances in the simulation of gauge theories with light dynamical quarks, and the ongoing spectacular progress in HPC hardware allow us to carry out precise studies of the dynamics of the strong interactions from first principles. We aim at computations of lattice quantities with a precision of a few percent. This is the accuracy required for the interpretation and the analysis of the wealth of experimental results expected both for sub-nuclear matter and for the quark-gluon plasma.