  A detailed tight-binding analysis of the electron band structure of the CuO_2
plane of layered cuprates is performed within a sigma-band Hamiltonian
including four orbitals - Cu3d_x^2-y^2, Cu4s, O2p_x, and O2p_y. Both the
experimental and theoretical hints in favor of Fermi level located in a Cu or O
band, respectively, are considered. For these two alternatives analytical
expressions are obtained for the LCAO electron wave functions suitable for the
treatment of electron superexchange. Simple formulae for the Fermi surface and
electron dispersions are derived by applying the Loewdin down-fold procedure to
set up the effective copper and oxygen Hamiltonians. They are used to fit the
experimental ARUPS Fermi surface of Pb_0.42Bi_1.73Sr_1.94Ca_1.3Cu_1.92O_8+x and
both the ARPES and LDA Fermi surface of Nd_2-xCe_xCuO_4-delta. The value of
presenting the hopping amplitudes as surface integrals of ab initio atomic wave
functions is demonstrated as well. The same approach is applied to the RuO_2
plane of the ruthenate Sr_2RuO_4. The LCAO Hamiltonians including the three
in-plane pi-orbitals Ru4d_xy, O_a 2p_y, O_b 2p_x and the four transversal
pi-orbitals Ru4d_zx, Ru4d_yz, O_a 2p_z, O_b 2p_z, are separately considered. It
is shown that the equation for the constant energy curves and the Fermi
contours has the same canonical form as the one for the layered cuprates.
