  We present in detail the procedure for calculating the heterotic one-loop
effective action. We focus on gravitational and gauge couplings. We show that
the two-derivative couplings of the gravitational sector are not renormalized
at one loop when the ground state is supersymmetric. Arguments are presented
that this non-renormalization theorem persists to all orders in perturbation
theory. We also derive the full one-loop correction to the gauge coupling. For
a class of $N=2$ ground states, namely those that are obtained by toroidal
compactification to four dimensions of generic six-dimensional $N=1$ models, we
give an explicit formula for the gauge-group independent thresholds, and show
that these are equal within the whole family.
