  We present an ab initio theory of transport quantities of metallic
ferromagnets developed in the framework of the fully relativistic tight-binding
linear muffin-tin orbital method. The approach is based on the Kubo-Streda
formula for the conductivity tensor, on the coherent potential approximation
for random alloys, and on the concept of interatomic electron transport. The
developed formalism is applied to pure 3d transition metals (Fe, Co, Ni) and to
random Ni-based ferromagnetic alloys (Ni-Fe, Ni-Co, Ni-Mn). High values of the
anisotropic magnetoresistance (AMR), found for Ni-rich alloys, are explained by
a negligible disorder in the majority spin channel while a change of the sign
of the anomalous Hall effect (AHE) on alloying is interpreted as a band-filling
effect without a direct relation to the high AMR. The influence of disorder on
the AHE in concentrated alloys is investigated as well.
