  We present an introduction to the mathematical theory of the Lagrangian
formalism for multiform fields on Minkowski spacetime based on the multiform
and extensor calculus. Our formulation gives a unified mathematical description
for the main relativistic field theories including the gravitational field
(which however will be discussed in a separate paper). We worked out several
examples (including tricks of the trade), from simple to very sophisticated
ones (like, e.g., the Dirac-Hestenes field on the more general gravitational
background) which show the power and beauty of the formalism.
