"The black hole at the centre of every massive galaxy bulge appears toplay a controlling role in the final stellar mass of that bulge. Thisis especially true for the most massive galaxies at the centres ofcool core clusters where X-ray observations clearly show energy beingfed back into the surrounding gas which would otherwise cool and formmore stars at high rates. Although the total energy budget for thisphenomenon is clear, the details by which the processes operate arenot. This proposal aims to further our understanding of how accretingblack holes generate and feed back energy into the surrounding gas,how it is dissipated and establishes a heating / cooling balance andhow the black hole, galaxy and feedback co-evolve. The work will focuson the broad iron line and X-ray reflection spectral and reverberationcomponents which we have discovered in the spectra of accreting blackholes, on X-ray imaging spectroscopy of cool core clusters of galaxiesand on the filamentary nebulosity commonly observed around the centralgalaxy in such clusters. The work will involve X-ray observationstogether with data from other wavebands where relevant. We shall alsoconsider theoretical aspects of the problem and interpretthe whole phenomenon. The current X-ray telescopes (Chandra, XMM andSuzaku) are now mature and we understand how to use them optimally,particularly with longer exposures. Major new data are coming fromNuSTAR (launched 2012), which is now opening up the hard X-ray band,and from ASTRO-H (to be launched 2014) which will open up the iron-Kband to high spectral resolution and thus direct measurement of thevelocity field of the hot and cold components of AGN Feedback."