In these lectures we will first provide the basics of simulations of Quantum Field Theory. We will see that the methods and concepts of such simulations are closely related to those of Condensed Matter Physics. The principle of local gauge invariance will, however, soon focus the attention to different systems which are studied in Quantum Field Theory, as compared to those considered in Condensed matter physics.
In the lectures we will give special emphasis to models containing fermionic degrees of freedom. We will point out the particular difficulties of simulations of such systems and discuss several algorithms to treat fermions numerically. We finally turn to recent developments which introduce non-local fermion actions, showing spectacular properties as far as chiral symmetry is concerned. We discuss numerical methods to treat such complicated fermion actions.