The course consists of two parts. 

I. Gauge theories beyond perturbation theory.

The first part of the course covers strongly interacting gauge theories and their phase structure. Methods include lattice field theory, numerical simulations and effective field theories. Simple models are used as examples or proposed as exercises.  The main goal is a general knowledge of the different phases of Quantum Chromo Dynamics, from confinement to extreme environment of temperatures and densities, with special attention to the physics of the early Universe within and beyond the Standard Model. The students will acquire a working knowledge  of lattice methods, also in view of applications of artificial intelligence and quantum computing.