This volume collects together summaries of work on a modern theory of black holes in terms of local notions, covering fields as diverse as classical and numerical general relativity, differential geometry, thermodynamics, quantum field theory, and quantum gravity. Existing textbooks define a black hole by an event horizon. However, its teleological nature means that it is epistemologically unsound, empirically unverifiable, even theoretically impractical and not directly related to local physics. The last decade or so has seen increasing evidence that more local notions are more useful and have understandable associated physics. There is heretofore no one volume which covers all the main aspects, hence the timeliness of this attempt. Each chapter is written by an expert or experts on a particular topic. It is intended for anyone interested in black holes, as a reference for the many applications and issues.