This monograph is devoted to a systematic exposition of the theory of extension of holomorphic functions, e. g. characterizations of envelopes of holomorphy with respect to various families of holomorphic functions. Therefore, there is emphasis on a detailed presentation of holomorphic convexity and pseudoconvexity of Riemann domains over Cn.

Our interest in this area of complex analysis started directly after our studies when both of us were interested in continuation of holomorphic functions. During the years we got the impression that there is a need to have a source where the main results could be found. We hope this book can serve as such a source. The choice of topics obviously reflects our personal preferences.