This thesis deals with the radiative emission arising out of the interaction of several core collapse supernovae (SNe) with their dense circumstellar medium (CSM) and uses the radiative properties as diagnostics of the ionized plasma in and around the interaction region. These supernovae include: SN 1993J, SN 1995N, SN 2002ap & SN 2003bg. In a SN explosion, the outer layers of the star are set in motion with high velocities and the collision of the ejecta with the CSM leads to a less dense and hot blast wave forward shock with velocities ~ 20,000 km/s and T ~ 109K. When the external layers of the expanding ejecta decelerate upon interaction with the CSM, a reverse shock develops that starts propagating into the stellar envelope, with velocity few times 1000 km/s relative to the expanding stellar ejecta, heating it to T ~ 107K. Forward shock velocities are typically 1000 times the speed of the wind that was being lost from the progenitor prior to the SN explosion. Consequently, evolution of the shock and the radiative properties of the SN few years after the explosion probes the history of the environment of the progenitor star thousands of years before the explosion. Interaction of the shocked ejecta with the CSM gives rise to emission in radio and X-ray bands. The emission in various wavebands arising due to this interaction usually has a slower decay rate than the initial photospheric emission arising from ionic recombination and radioactive decay. Hence, one is usually able to track the supernovae for longer time. Radio emission is generated from the forward shocked shell due to the synchrotron emission by relativistic electrons in the presence of the strong magnetic fields. The strong magnetic field in the shocked shell is believed to be generated by Rayleigh Taylor instability, which enhances any seed magnetic field present initially. Relativistic electrons are produced, most likely, by shock mediated acceleration processes. The early rapid rise in the radio flux density results from the shock overtaking progressively further into the progenitor’s stellar wind and therefore in the regions of decreasing optical depth. Since optical depth is larger at lower frequencies lower frequencies turn on later in time. The emission from the shocked region decreases slowly with time as the shock expands, so even when the radio absorption has become negligible, the radio light curve would show this decline. Radio emission is absorbed initially by different mechanisms depending upon the mass loss rate in the progenitor wind, shock velocity, electron temperature etc. If the emission is absorbed by an electron moving in the field of an ion (free-free absorption), then one can infer the mass loss of the progenitor. If on the other hand, the radio emission is absorbed by synchrotron self absorption in which the photon interacts with an electron in a magnetic field, then it gives information about the size of the emitting region. In contrast, X-ray emission initially comes from the forward shock and is non-thermal in nature. The X-rays could be either due to synchrotron emission or due to inverse Compton scattering in which the photospheric optical photons can be boosted to X-ray energies due to multiple scattering with the electrons. Late time X-rays, which are thermal in nature, arise from the reverse shock and probe the CSM interaction of the SN ejecta and provide information of the plasma and surroundings. However, in an alternate model due to Chugai (1993, Astron. Rep., 41, 672), X-rays can also emerge from the radiative cooling of the shocked, dense clumps (clouds) embedded in the circumstellar wind overtaken by the blast-wave shock and crushed by the pressure of the strongly shocked wind. Line-widths, elemental yields and luminosity curves are the observational signatures to distinguish between the two models. X-ray spectra of SNe can be used to determine what elements are there in the shock heated ejecta, the supernova’s nucleosynthetic yield and thence the (helium) core mass of the progenitor at the explosion stage. Nucleosynthetic studies of SNe and constraints on their progenitor masses are of vital interest to the origin and distribution of elements in the galaxy and its chemical evolution. Chapter 1 gives a general overview of supernova types, explosion scenarios and essentials of shock dynamics in the CSM. Chapter 2 gives an overview of the radiative processes relevant to radio and X-ray emission. I describe the radio and X-ray data analysis procedures in Chapter 3. I discuss synchrotron aging in young supernovae in Chapter 4. Synchrotron aging has been seen in many old sources, such as radio galaxies, Compact Steep Spectrum sources etc., where the age of the source is not known. Synchrotron aging was used to determine the age of such sources using magnetic field under equipartition (between magnetic energy density and relativistic energy density) as an input parameter. However in young supernovae (whose ages are known), the magnetic fields are generated due to the instabilities (Rayleigh Taylor) created in the plasma and hence it is difficult to estimate the field correctly. Here synchrotron aging can be used to derive the magnetic field independent of any assumption of equipartition. I discuss the synchrotron aging in detail and derive a significant conclusion about the plasma energetics from the combined GMRT and Very Large Array (VLA) spectrum of a 10 year old type IIb SN 1993J around day 3200 after explosion. I found a steepening of its spectrum caused by synchrotron aging. After taking into account the adiabatic losses and Fermi acceleration of electrons, I estimate from the synchrotron break, the magnetic field in the plasma and derive that the magnetic energy density is 10,000 times larger than the relativistic energy density. In Chapter 4, I also underscore the importance of wide band radio spectrum in dealing with issues of the physics of shocked plasma. In Chapter 5, I describe further studies of SN 1993J with the GMRT at frequencies 1420, 610, 325 and 235 MHz, from 7.5 years to 10 years since explosion. SN 1993J is a unique supernova for which magnetic field and sizes are determined from model independent measurements; the former from the synchrotron cooling break and the latter from VLBI measurements. Using GMRT spectra and earlier published spectra of SN 1993J, I compare the VLBI sizes of the SN 1993J with that of obtained from the peak of the spectra using synchrotron self absorption (SSA) model. I find that the SSA sizes are roughly equal to the VLBI sizes of the SN. This suggests that the synchrotron self absorption is responsible for the turn over in the spectra of SN 1993J at all the epochs. The size evolution shows that the ejecta expands freely initially and then show a small deceleration in the later epochs. I also plot the magnetic field evolution, which goes as Spectral index initially lies between 0.8 - 1.0 and later seems to flatten with time and lies within the range of 0.5 - 0.7. The mass loss rate roughly remains constant ( ~ 5 x 10−5M yr−1) in two years of GMRT observations, i.e., 8000-10,000 years before explosion. Light curves based on high frequency existing models extrapolated to low frequencies overpredict the flux densities at low frequencies. Some extra opacity is needed to incorporate the difference. This suggests that the low frequency opacity in SN 1993J is not a simple extrapolation of high frequency opacity and a hitherto unaccounted for absorption may be at work at low frequencies. I describe the Chandra X-ray observatory work on SN 1995N, which we observed on March 28, 2004, in Chapter 6. I detected the X-ray emission from the SN with most of the emission found to be below 2 keV. SN 1995N had also been observed by ROSAT and ASCA earlier on three occasions. Our reanalysis of ASCA 1998 spectra revealed certain line features which were not reported in the published work of Fox et al. (2000, MNRAS, 319, 1154). I detect a Ne X line in both ASCA and Chandra observations, and while I detect a Ne IX line in the Chandra observation this was absent in the ASCA one. At the same time I detect a 1.3 keV line in the ASCA observation, absent in the Chandra spectrum of SN 1995N. No Fe line was detected in either spectrum. The light curves of SN 1995N suggested a non-linear profile due to high ASCA flux. We re-analyzed the ASCA data in view of the high-resolution imaging data obtained by Chandra and found at least ten more sources contributing to the SN flux due to the large ASCA PSF. After taking out the contribution from the contaminating sources, the light curve appears to be consistent with a linear decline. This indicates that the X-ray emission is due to the reverse shock going through a shallow ejecta profile. I also find that the absorption column density is at least 2.5 times more than that calculated from the galactic extinction maps. This suggests that the moderate, extra absorption is likely to be due to the formation of a thin cool ejecta-shell between reverse-shock and the contact discontinuity. About 0.01 M of Ne is estimated to be present in SN 1995N from the Chandra line detection. This, most likely, arises in the partially burnt He core at velocities > 5000 km s−1 . I also observed SN 1995N with the GMRT in radio bands. I describe these results in Chapter 7. The spectrum is seen to be peaking towards lower frequencies with the time. The radio light curve suggests that the SN is already in the optically thin part of the light curve. Some but not all type Ic supernovae have shown association with Gamma Ray Burst (GRB) sources. This seems to divide the type Ic SNe in two subclasses -the ones associated with GRBs and the ones without the GRB connection. The observations of these two classes of type Ic SNe and their comparison (the ”afterglows”) are likely to be useful in determining the physical conditions inside the progenitor star which leads some of the type Ic supernovae to have GRB associations. Since these SNe are bare core SNe with no hydrogen and little or no helium envelope, their prompt emission in the radio and high energy bands provide the most promising probes of their interior at early times. In Chapter 8, I investigate the origin of prompt X-ray emission in a type Ic supernova SN 2002ap, a non-GRB supernova. An analysis of SN 2002ap, observed with XMM-Newton on Feb 3, 2002 as a Target Of Opportunity is presented and spectral model fits to the prompt X-ray emission are obtained. I model the early X-ray emission with inputs from optical photometry and light curve and find that multiple inverse Compton scattering of optical photons from the supernova photosphere by electrons in the medium can account for the observed early X-ray flux and its spectrum for modest electron temperatures and optical depths. I compare the X-ray image with the GMRT 610 MHz radio image obtained three days apart. While I find no radio counterpart of the SN at such low frequencies, several sources in the field have radio and X-ray counterparts. I compare the radio data obtained from three different supernovae in their early phases and model these using the synchrotron self absorption model. GRB associated SN 1998bw was found to be most rapidly expanding with fastest transition from optically thick to optically thin part in the spectrum. Radio studies of SN 2003bg, another type Ic supernova is discussed in Chapter 9. I observed SN 2003bg with the GMRT from day 43 till day 600 since explosion. On one occasion (day ~ 350), I combined the GMRT data with the VLA data to get a composite spectrum. From the optically thick part of the spectrum, I find that the dominant absorption mechanism in the SN is synchrotron self absorption. I deduced magnetic field and size of the supernova under the assumption of equipartition. I discuss the overall results in Chapter 10. In this thesis, I have investigated four supernovae in detail and few more have been observed with lesser sampling frequency (see Chapter 10 and P. Chandra et al 2002, BASI 30, 755). Although they all belong to the ejecta dominated free expansion phase, the core-collapse supernovae are of widely different subclasses and I have observed them at very young ages (few days) to more than 10 years of age, with multiple probes, going through a variety of emission mechanisms and absorption processes. I provide comparison between different supernovae observed by us and others. In cases, where I am able to obtain X-ray spectra, nucleosynthesis arguments lead me to constrain the mass of the progenitor star and the composition of its layers.