  In this paper some techniques useful to perform quantum field theory
computations in a covariant manner are reviewed. In particular the background
field gauge, the zeta function regularization and the heat kernel approach are
highlighted. Some detailed calculations of the Schwinger-de Witt coefficients
of the small proper time expansion of the heat kernel are also repeated in
detail. This work reports lectures given by Enrique \'Alvarez at the
IFT-UAM-CSIC in Madrid.
