  We develop a theory of the anisotropic magnetoresistance (AMR) effects of
arbitrary directions of current and magnetization for ferromagnets. Here, we
use the electron scattering theory with the $s$--$s$ and $s$--$d$ scattering
processes, where $s$ is the conduction electron state and $d$ is the localized
d states. The resistivity due to electron scattering is expressed by the
probability density of the d states of the current direction. The d states are
numerically obtained by applying the exact diagonalization method to the
Hamiltonian of the d states with the exchange field, crystal field, and
spin--orbit interaction. Using the theory, we investigate the transverse AMR
(TAMR) effect for strong ferromagnets with a crystal field of cubic or
tetragonal symmetry. The cubic systems exhibit the fourfold symmetric TAMR
effect, whereas the tetragonal systems show the twofold and fourfold symmetric
TAMR effect. On the basis of the above results, we also comment on the
experimental results of the TAMR effect for Fe$_4$N.
