The Mathematical Apparatus for Quantum-Theories : Springer : 9783642460326 : 3642460321 : 09 Mar 2012 : The purpose of this book is to ,give the theoretical physicist a geometrical, visual and precise mathematical apparatus which would be better adapted to some of their arguments, than the existing and generally applied methods. The theories, presented in this book, are based on the theory of Boolean lattices, whose elements are closed subspaces in the separable and complete Hilbert-Hermite-space. The first paper, in which the outlines of the said mathematical apparatus is sketched, is that of the author: "Un nouvel appareil mathematique pour la theorie des quanta."] The theory exhibited in this paper has been simplified, generalized and applied to several items of the theory of maximal normal operators in Hilbert-space, especially to the theory of multiplicity of the continuous spectrum and to permutable normal operators, based on a special canonical representation of normal operators