"Galaxy clusters are the largest gravitationally bound systems in the Universe and often host the largest galaxies (known as the brightest cluster galaxies (BCG)) at its centers. These BCG’s are embedded in hot 1-10 keV X-ray gas. A subset of galaxy clusters known as cool-core clusters show sharply peaked X-ray emission and high central densities, demonstrating cooling of the surrounding halo gas in timescales much shorter than a Hubble time. These observations led to the development of a simple cooling flow model. In the absence of an external heating process, a cooling flow model predicts that the hot intracluster medium gas in these dense cores would hydrostatically cool, generating cooling flows in the center of the cluster. This cooled gas will eventually collapse to form stars and contribute to the bulk of galaxy mass. The rates of star formation actually observed in the clusters however are far less than predicted by the cooling flow model, suggesting a non-gravitational heating source. Active galactic nuclei (AGN), galaxies hosting a supermassive black hole that ejects outflows via accretion, is currently the leading heating mechanism (referred to as AGN feedback) explaining the observed deficit in the star formation rates. AGN feedback also offers an elegant explanation to the observed black hole and galaxy co- evolution. Much of the evidence for AGN feedback has been obtained from studies focussed on galaxy clusters and luminous massive systems with little evidence that it occurs in more typical systems in the local universe. Our research investigates this less explored area to address the importance of AGN heating in the regulation of star formation in typical early type galaxies in the local universe. We selected a sample of 200+ early type, low redshift galaxies and carried out a multiple wavelength study using archival observed in the UV, IR and radio. Our results suggest that early type galaxies in the current epoch are rarely powerful AGN and AGN feedback is constrained to be low in our sample of low redshift, typical early type galaxies. Although heating from the AGN is powerful enough to suppress the cooling of the hot gas, it does not completely offset gas cooling at all times and substantial cooler gas exists in the cores of some galaxy clusters (cool-core clusters), the gas properties of which are not explained by AGN heating models alone. The second part of our research focuses on unravelling the mystery of the unknown heating source regulating star formation in galaxy clusters. We have obtained deep FUV spectroscopy using the HST cosmic origins spectrograph of two cool-core clusters A2597 and Zw3146. FUV spectral lines provide the much needed diagnostics capable of discriminating between various heating models, which was difficult with the standard optical line diagnostics. We investigate several heating/ionization mechanisms namely stellar photoionization, AGN photoionization, and shock heating. We use pre-run Mappings III photoionization code results to model the ionizing radiation field. In general, we notice that there is no one single model that provides a satisfactory explanation for the ionization state of gas. How- ever, we show that stellar and AGN photoionization alone are not enough to ionize the nebula in A2597 and speculate that, shock heating is the likely ionizing source."--Abstract.