The text introduces the reader to an area of theoretical elementary particle physics which has been the subject of intensive research since the 1970s. Its purpose is to provide graduate students with basic theoretical knowledge of quantum field theories, formulated on a time-space lattice, as well as the computational tools for carrying out research in this field. Special emphasis is placed on explaining in detail many concepts which students have problems with when atending for the first time a course on lattice guage field theories. The material covered should enable the reader to follow the vast amount of literature on this subject without too much difficulty.
The path integral approach to quantization; the free Scalar field on the Lattice; fermions on the Lattice; Abelian gauge fields on the Lattice and compact QED; non-Abelian gauge fields on the Lattice, compact QCD; the Wilson Loop and the static quark-antiquark potential; the QQ potential in some simple models; the continuum limit of Lattice QCD; Lattice action and energy sum rules; strong coupling expansion; the Hopping parameter; expansion; weak coupling expansion (I); weak coupling expansion (II) - Lattice QED; weak coupling expansion (III) - Lattice QCD; Monte Carlo methods; some results of Monte Carlo calculations; introduction to finite temperature field theory - path integral representation of the partition function; finite temperature perturbation theory off and on the Lattice; non-perturbative QCD at finite temperature; the high temperature phase of QCD. (Part contents).