  The main principles of two-dimensional quantum field theories, in particular
two-dimensional QCD and gravity are reviewed. We study non-perturbative aspects
of these theories which make them particularly valuable for testing ideas of
four-dimensional quantum field theory. The dynamics of confinement and theta
vacuum are explained by using the non-perturbative methods developed in two
dimensions. We describe in detail how the effective action of string theory in
non-critical dimensions can be represented by Liouville gravity. By comparing
the helicity amplitudes in four-dimensional QCD to those of integrable
self-dual Yang-Mills theory, we extract a four dimensional version of two
dimensional integrability.
