Like quantum computing or DNA computing, membrane computing is an unconventional model of computation associated with a new computing paradigm. The field of membrane computing was initiated in 1998 by the author of this book; it is a branch of natural computing inspired by the structure and functioning of the living cell and devises distributed parallel computing models in the form of membrane systems, also called P systems. This book is the first monograph surveying the new field in a systematic and coherent way. It presents the central notions and results: the main classes of P systems, the main results about their computational power and efficiency, a complete bibliography, and a series of open problems and research topics. Thus, the book is indispensible reading for anybody interested in molecular computing.Paun, Gheorghe is the author of 'Membrane Computing An Introduction' with ISBN 9783540436010 and ISBN 3540436014.