Euclidean quantum field theory

This talk deals mainly with two aspects of Euclidean quantum field theory, one related to the problem of mathematical construction, the other related to the problem of physical interpretation. For the problem of the construction, methods based on the deep analogy between Euclidean quantum field theory and classical statistical mechanics are emphasized. In particular the lattice approximation strategy and its applications are described. For the problem of physical interpretation the main ideas of a proposal, according to which the Euclidean field theory can be interpreted as a stochastic field theory in the physical Minkowski space-time, are sketched. (Auth.)