Semiclassical and stochastic gravity : quantum field effects on curved spacetime The two pillars of modern physics are general relativity and quantum field theory the former describes the large scale structure and dynamics of space time the latter the microscopic constituents of matter. Combining the two yields quantum field theory in curved space time which is needed to understand quantum field processes in the early universe and black holes such as the well known Hawking effect. This book examines the effects of quantum field processes back reacting on the background space time which become important near the Planck time (10 43 sec). It explores the self consistent description of both space time and matter via the semiclassical Einstein equation of semiclassical gravity theory exemplified by the inflationary cosmology and fluctuations of quantum fields which underpin stochastic gravity necessary for the description of metric fluctuations (space time foams). Covering over four decades of thematic development this book is a valuable resource for researchers interested in quantum field theory gravitation and cosmology