Abstarct: In this thesis, nanocomposites with the general formula (1-x)BiFeO3-(x)AFe2O4 ) A=transition mextal, TM (were synthesized via the auto-combustion technique, employing varying stoichiometric ratios denoted by x (specifically: 0.0, 0.2, 0.5, and 1). X-ray diffraction (XRD) patterns of the synthesized samples revealed a rhombohedral perovskite structure, indexed to the R3c space group, for the pristine BiFeO3 sample. Conversely, the CoFe2O4, NiFe2O4, and Co0.5Ni0.5Fe₂O₄ samples exhibited a face-centered cubic (FCC) structure, consistent with the Fd-3m space group. Structural characterization and elemental analyses confirmed the formation of the fabricated nanocomposites. The estimation of the average crystallite size for the (1-x) BiFeO₃-(x) CoFe₂O₄ nanocomposites revealed a discernible reduction in crystallite dimensions within both the BiFeO3 and CoFe2O4 phases. FESEM micrographs demonstrated a discernible alteration in the morphology of the composite samples relative to their pure counterparts. Transmission Electron Microscopy (TEM) analysis of the samples further elucidated the development of a core-shell architecture. The examination of the dielectric properties of the samples revealed that the BiFeO₃ 80 wt% - CoFe₂O₄ 20 wt% composite exhibits a high dielectric constant, low loss, good conductivity, and superior electrochemical properties. Employing the Kobelka-Munk method, the energy band gaps of the BiFeO₃, CoFe₂O₄, BiFeO₃ 80 wt%-CoFe₂O₄ 20 wt%, and BiFeO₃ 50 wt%-CoFe₂O₄ 50 wt% samples were determined to be 1.42 eV, 1.43 eV, 1.39 eV (indirect), and 2.62 eV (direct), respectively. The structural, dielectric, and optical properties of (1-x) BiFeO₃-(x)NiFe₂O₄ nanocomposites were investigated. Analysis of the FESEM images indicated that the BiFeO₃ 50 wt%-NiFe₂O₄ 50 wt% sample exhibited a smaller average particle size compared to the other samples. The energy loss observed in this sample was lower than that of the BiFeO₃ 80 wt%-NiFe₂O₄ 20 wt% sample, thereby establishing it as the optimal composition within this class of nanocomposites. The indirect band gap values for NiFe₂O₄, BiFeO₃ 80 wt%-NiFe₂O₄ 20 wt%, and BiFeO₃ 50 wt%-NiFe₂O₄ 50 wt% are 1.76 eV, 2.21 eV, and 2.10 eV, respectively. The (1-x) BiFeO₃-(x) Co0.5Ni0.5Fe2O4 composites were found to have optimal dielectric performance in the BiFeO₃ 80 wt%- Co0.5Ni0.5Fe2O4 20 wt% composition. Electrochemical impedance analysis indicated a reduction in grain boundary resistance for the BiFeO₃ 50 wt%- Co0.5Ni0.5Fe2O4 50 wt% and BiFeO₃ 80 wt%- Co0.5Ni0.5Fe2O4 20 wt% samples. The magnetic characterization of the CoFe₂O₄, NiFe₂O₄, and Co0.5Ni0.5Fe2O4 samples indicated soft ferromagnetic behavior. The presence of AFe₂O₄ improved the overall magnetic properties of the composites.