This book has two important merits. First it contains a unifying theory of what has been done in the direction of generalizing the notion of nuclearity, replacing the space l1 by an arbitrary sequence space [lowercase Greek]Lambda. Second, written very clearly, it is quite understandable for non-specialists, and can thus serve as a starting point for those who become interested in the subject. The book contains new material, gives answers to existing conjectures, and discusses several unsolved problems. It is indispensable for those who are doing research in this domain.