  We present a pedagogical exposition of some applications of functional
methods in quantum field theory: we use heat-kernel and zeta-function
techniques to study the Casimir effect, the pair production in strong electric
fields, quantum fields at finite temperature and beta-functions for a
self-interacting scalar field, QED and pure Yang-Mills theories. The more
recent application to the UV/IR mixing phenomenon in noncommutative theories is
also discussed in this framework.
