High dielectric constant materials have tremendous impact on miniaturization of devices that are used in various applications like wireless communication systems, microelectronics, global positioning systems, etc. To store electric charge in a very small space necessarily needs a capacitor with very high dielectric constant. Thus, these materials are very important in fabricating capacitors, or metal oxide semiconductor filed effect transistor (MOSFET). Among the existing commercially available devices, silicon-based microelectronic devices are commonly used based on the moderately stable dielectric constants of silicon with low losses and minimal temperature and frequency dependence. However, now-a-days, the perovskite based transition metal oxides have drawn attention that have the ability to fulfill all the requirements for being a good dielectric material in all the industrial applications. In this thesis we have studied a few selected perovskite based transition metal oxide systems in terms of their dielectric and magnetic behaviour. In Chapter 1, we have have given brief introductions about the some application of dielectric materials and the origin of dielectric and magnetic properties in the materials. We have also discussed about the polarisation in the dielectric materials to understand it’s frequency dependence and also to formalise different relaxation behaviour with the help of physical and mathematical explanation. In Chapter 2, we describe the various methodologies adopted in this thesis. In Chapter 3, we have studied the dielectric behaviour of Nd2NiMnO6, a rare earth based double perovskite ferromagnetic insulator. We successfully synthesised and characterised the compounds, settled the valency issues with the help of temperature dependent XAS of the transition metal atom in contrast to the existing controversy available in literature. We have found that this material shows relaxor kind behaviour with a colossal dielectric constant value. We have studied in details the origin of the colossal dielectric constant and the relaxation behaviour along with the a.c and d.c. transport properties. We have shown the origin of the ferromagnetism (TC ∼ 200 K) with a low temperature antiferromagnetic ordering (TN ∼ 55 K) with the help of detailed studies of temperature dependent d.c., a.c. magnetism and their XMCD. We have also investigated the isothermal variation of magnetodielectric and magnetoresistance behaviour as a function of magnetic field and their origin. In Chapter 4,we study the effect of cation anti-site disorder on the magnetic, dielectric and transport properties of another rare earth based ferromagnetic double perovskite insulator La2NiMnO6 by controlling different extent of anti-site disordered. We have confirmed the valency of the transition metal cations using XAS technique and followed by shown, different types of magnetic interaction between the transition metal cations using d.c magnetic, quantitative XMCD analysis and the origin of large dielectric response, a.c. transport & dielectric relaxation using temperature variation dielectric measurement as an experimental evidence in contrast of our previous speculation published in literature. We further have studied, the coupling between the magnetic and electric spin through isothermal magnetodielectric measurement. In Chapter 5, we have successfully synthesised and characterised a solid solution of YMnxIn1−xO3 series via different mol % of In doping in the multiferroic YMnO3 system. YMnO3 is a well known multiferroic material studied rigorously during past few decades. We have seen, YMnO3 which has a antiferromagnetic ordering temperature of ∼ 75 K suppressed with increasing the dopant concentration In. We have figured out the effect of In doping in the suppression of multiferroic phase and extended it to the dielectric properties. We have found that, the temperature dependence of dielectric constant shows an anomaly at the magnetic ordering temperature and studied magnetodielectric coupling. We have also investigated the temperature variation of dielectric relaxation and a.c. transport behaviour as a function of composition. In Chapter 6, we have identified the phase seperation and proposed a phase diagram as function of Gd doping in the Ho2−xGdxCuTiO6 double perovskite, where two end member, namely Ho2CuTiO6 and Gd2CuTiO6 are found to be in two different crystallographic phase as, hexagonal (P63cm) and orthorhombic (Pnmm), respectively. We have characterised the valency of the transition metal cations using XAS.We have seen very less temperature and frequency dependence of dielectric constant in hexagonal phase in compare to the orthorhombic phase and tried to figuring out from experimental analysis by performing temperature dependence dielectric const measurement. We also have shown the effect of doping in the origin of dielectric relaxation, a.c transport and magnetic behaviour of this system. In Chapter 7, we have synthesised and characterised successfully two different rare earth based layered perovskite La3Cu2VO9 and La4Cu3MoO12 compounds are of centrosymmetric space group. We have figured it of the valency of the different atoms present in the compound using XAS. We also do have observed the good temperature stability of dielectric constant of these materials and explored origin of mechanism in the dielectric relaxation, a.c. transport property by performing the temperature dependance dielectric measurement. The magnetic structure also have shown with the help of d.d. magnetic measurements. In Appendix A, we have seen the very stable dielectric constant constant from very low to above room temperature of the 2D nano PbS. The frequency stability of dielectric constant is also remarkable in compare to bulk PbS values available in literature. We have explored the origin of the conductivity and relaxation mechanism performing dielectric constant measurement. In conclusion, we investigate, in this thesis, dielectric properties of different transition metal oxides system and the mechanism of dielectric relaxation, a.c, d.c transport and their origin of magnetic response.