Extension problems in complex and CR-geometry

[Excerpt from the introduction]: The aim of this thesis work is to present some of the many different extension problems that were considered in complex and CR-geometry, starting from well-known classical ones, up to the very recent still unpublished results and to the still open problems. This is going to be a (partial, since the subject is so broad) survey on the extension problems. There is neither presumption of completeness, nor a judgement on the importance of the arguments chosen, since the choice of the arguments treaten, a very personal one, simply arose from my interests of research and my mathematical experience of the last few years.