  In these lectures we provide a short introduction to the Monte Carlo
integration method and its applications. We show how the origin of ultraviolet
divergences if Field Theories is in the undefined formal product of
distributions and how one can define the Path Integral in terms of regularized
distributions in order to cancel these divergences. This technique provides the
only non perturbative regularization procedure of continuum Field Theories and,
at the same time, provides a practical method to compute correlation (Green)
functions (using Monte Carlo integration for the regularized path integrals).
We then apply these tools to formulate QCD on a lattice. Some of the examples
are accompanied by complete computer programs.

High Energy Physics - Lattice;Computational Physics;Quantum Physics