This dissertation describes calculations of the magnetization dependence of the intrinsic

Hall conductivity in three elemental ferromagnets: iron, cobalt and nickel. We compare our

calculations with experimental measurements of these anomalous Hall coefficients, and

we show that ab initio calculations of the anomalous Hall conductivity from the Karplus-

Luttinger theory explain the observed changes in the anomalous Hall coefficients of these

metals as the magnetization direction is varied.