  Two-component spinors are the basic ingredients for describing fermions in
quantum field theory in four space-time dimensions. We develop and review the
techniques of the two-component spinor formalism and provide a complete set of
Feynman rules for fermions using two-component spinor notation. These rules are
suitable for practical calculations of cross-sections, decay rates, and
radiative corrections in the Standard Model and its extensions, including
supersymmetry, and many explicit examples are provided. The unified treatment
presented in this review applies to massless Weyl fermions and massive Dirac
and Majorana fermions. We exhibit the relation between the two-component spinor
formalism and the more traditional four-component spinor formalism, and
indicate their connections to the spinor helicity method and techniques for the
computation of helicity amplitudes.
