Lattice Gauge Theories and Yang-Mills Theories are probabilistic models used to give some discrete, Euclidean approximation to the continuum Quantum Field Theories of interest, such as Quantum Electrodynamics and Quantum Chromodynamics. The central question in this field and mathematical physics is to establish a continuum limit as the lattice spacing is taken to 0.

In this minicourse, we will start by giving the physical motivation for Lattice Yang-Mills Theory and discuss the central observables of interest. Afterwards, we will begin to present some of the recent progress in this field.