  Many complex systems are characterized by intriguing spatio-temporal
structures. Their mathematical description relies on the analysis of
appropriate correlation functions. Functional integral techniques provide a
unifying formalism that facilitates the computation of such correlation
functions and moments, and furthermore allows a systematic development of
perturbation expansions and other useful approximative schemes. It is explained
how nonlinear stochastic processes may be mapped onto exponential probability
distributions, whose weights are determined by continuum field theory actions.
Such mappings are madeexplicit for (1) stochastic interacting particle systems
whose kinetics is defined through a microscopic master equation; and (2)
nonlinear Langevin stochastic differential equations which provide a mesoscopic
description wherein a separation of time scales between the relevant degrees of
freedom and background statistical noise is assumed. Several well-studied
examples are introduced to illustrate the general methodology.
