  The effective Hamiltonian for perovskite titanates is derived by taking into
account the three-fold degeneracy of $t_{2g}$ orbitals and the strong
electron-electron interactions. The magnetic and orbital ordered phases are
studied in the mean-field approximation applied to the effective Hamiltonian. A
large degeneracy of the orbital states in the ferromagnetic phase is found in
contrast to the case of the doubly degenerate $e_g$ orbitals. Lifting of this
orbital degeneracy due to lattice distortions and spin-orbit coupling is
examined. A general form for the scattering cross section of the resonant x-ray
scattering is derived and is applied to the recent experimental results in
YTiO$_3$. The spin wave dispersion relation in the orbital ordered YTiO$_3$ is
also studied.
