  We present a formalism for the calculation of multi-particle one-loop
amplitudes, valid for an arbitrary number N of external legs, and for massive
as well as massless particles. A new method for the tensor reduction is
suggested which naturally isolates infrared divergences by construction. We
prove that for N>4, higher dimensional integrals can be avoided. We derive many
useful relations which allow for algebraic simplifications of one-loop
amplitudes. We introduce a form factor representation of tensor integrals which
contains no inverse Gram determinants by choosing a convenient set of basis
integrals. For the evaluation of these basis integrals we propose two methods:
An evaluation based on the analytical representation, which is fast and
accurate away from exceptional kinematical configurations, and a robust
numerical one, based on multi-dimensional contour deformation. The formalism
can be implemented straightforwardly into a computer program to calculate
next-to-leading order corrections to multi-particle processes in a largely
automated way.
