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Unlike the binary compound, where the simple charge transfer between cation and anion, or the ternary compound, which is composed of two binary compound semiconductors with a common cation or anion and whose electronic structures usually can be derived from those of the two constituent binary compounds with some modifications, the electronic property of quaternary compound is quiet complicated and interesting because of its complex charge transfer due to the electronegativity differences of its composed atoms. In this thesis, the first-principles pseudofunction (PSF) method and the first-principles molecular dynamics (MD) method are used to investigate the complicated variations of the electronic properties of three kinds of quaternary compounds, namely titanates [Ba1-xSrxTiO3 (BSTO) and Pb1-xSrxTiO3 (PSTO)], manganites [La1-xSrxMnO3 (LSMO) and La1-xCaxMnO3 (LCMO)], and (SiC)1-x(AlN)x. First, for BSTO and PSTO titanates, the first-principles calculation results and O K-edge x-ray absorption near edge structure (XANES) measurements are used to study their electronic structures. Because the valence band maximum (VBM) and conduction band minimum (CBM) are composed of O-p and Ti-d partial densities of states (PDOS), respectively, the bowing upward of calculated band gaps are related to the bowing downward of the Ti-O bond lengths for both of BSTO and PSTO, though for PSTO Pb-p PDOS also contributes to states near CBM. The substitutions of Sr by Ba in BSTO and by Pb in PSTO are quiet different, and it is because Pb atom has two extra valence electrons and a larger electronegativity than other cations. Second, we provide a new interpretation of the insulator-like to metal-like and anti-ferromagnetic to ferromagnetic transitions with Sr and Ca doping concentrations of La1-xSrxMnO3 and La1-xCaxMnO3, which is based on the variations of the Sr and Ca induced delocalization of the Mn majority-spin eg subband and the lowering of the Mn minority-spin t2g subband down to the Fermi energy (EF). Moreover, this study also suggests that the magnetic properties of manganites result from a detailed balancing between the O-mediated super-exchange mechanism that favors anti-ferromagnetism and the delocalized-state mediated Mn-spin coupling that favors ferromagnetism. Third, for (SiC)1-x(AlN)x superlattice, where SiC and AlN layers arranged alternatively along a common c-axis, our analysis shows subtle charge transfer among Si, C, Al and N ions and the band gap is not linear but bows downwards with respect to x. The calculated results suggest that the direct band gap of (SiC)1-x(AlN)x can be tuned over a wide range from 2.97eV to 6.28eV. Thus, (SiC)1-x(AlN)x is potentially useful for optoelectronic applications. It can be inferred from the calculated electronic properties of the above three kinds of quaternary compounds, the subtle charge transfer is because of differing electronegativities of constituent atoms, especially cations, and the relative valence state of the dopant with respect to the host cation. The subtle charge transfer also influences the magnetic properties of these hole-doped manganites. Moreover, the quaternary compounds have four kinds of atoms with different electronegativities and relative orbital energies, the complicated competition and balancing between the occupation of orbitals and charge transfer render the electronic properties of these material unable to be predicted from constituent binary oxides/semiconductors or even ternary compounds. For example, even though Pb substitutes Sr only in Pb1-xSrxTiO3, the effective charges of Ti and O are significantly altered.