Electronic structures and spectral functions of 3d transition metal (TM) oxides are theoretically investigated using a finite size cluster model. We first study the resonant 3d, 3p and 33 photoemisson spectroscopies (PES) at TM 2p threshold in late 3d TM monoxides and Ti0 2 using a cluster model with a TM ion and its ligand oxygen ions which includes the configuration interaction and the 3d-3d and 3d-core hole multipole interaction. Analyzing the experimental valence band spectra, we determine the charge transfer energy and the 3d-3d Coulomb interaction energy and show that the spectra give reliable information about the characteristic parameters of TM oxides. We also discuss the difference in the selection rule between the direct process and the resonance process. We next discuss the 3d PES, 3d inverse photoemission spectroscopy (IPES) and Cu 2p X-ray photo emission spectroscopy (XPS) spectra for the CU02 plane in the undoped and doped high-T c superconductors using a CUn Om cluster model containing up to four Cu ions. The model takes into account full degeneracy of the Cu 3d and 0 2p orbits and on-site Cu 3d-3d and 0 2p-2p electrostatic multipole interaction. For the 3d PES spectra of the undoped cluster, the main peak structure consists of two kinds of states. One has an excess hole introduced by the photoexcitation on nearest neighbor oxygen sites of the photo excited Cu site. The other has the hole on neighboring CU04 units, having the Zhang-Rice singlet state on the neighboring units. Because of the non-local character of the state corresponding to the main peak structure, the structure is sensitive to the number of the nearest neighbor Cu site. The interference of the initial and final state wave functions caused by the inter-Cu04-unit charge transfer lead to a spectral weight transfer to the low binding energy side. For the Cu 2p XPS spectra for undoped systems, a hole escaping from the core hole Cu site exhibits similar way and its main peak structure consists of the two kinds of screened states. In the light of calculations for larger clusters, the results obtained from the above small clusters are reinterpreted. For the 3d PES spectra of the electron doped cluster, two kinds of states are created inside the insulating gap and the chemical potential moves into the conduction band. The spectral weight is transferred to the peaks corresponding to the states created inside insulating gap, drastically. We furthermore present a formalism for a systematic basis set reduction of clusters. Using this formalism, we calculate the spectra of the clusters containing up to five Cu ions, where the number of basis set without the reduction beyond the tractable limit. We show that our formalism is a promising method to discuss spectral functions in large clusters including 3d TM ions other than Cu ion.